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  • On the spectra of a class of self-affine measures on R2
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-15
    Zhi-Min Wang

    For i∈{1,2}, let 0<|ρi|<1. For an expanding real matrix M=diag[ρ1−1,ρ2−1] and a three-element digit set D⊂Z2 with cardinality |D|, let μM,D be the self-affine measure defined by μM,D(⋅)=1|D|∑d∈DμM,D(M(⋅)−d). Let F32:=13{(l1,l2)t:l1,l2∈N+,0

    更新日期:2020-06-25
  • A priori estimates for D4 and F4 Toda systems
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    Debabrata Karmakar; Chang-Shou Lin; Zhaohu Nie

    In this article we establish the a priori bounds of the Toda systems with arbitrarily many singular sources associated to the simple Lie algebras of type D4 and F4, extending the previous works of Lin et al. [27], [20], [24] for the An,Bn,Cn and G2 type Lie algebras. The problem of obtaining a priori estimates can be reduced to locating the local mass of blowup solutions. The key step is to calculate

    更新日期:2020-06-23
  • Boundedness properties in a family of weighted Morrey spaces with emphasis on power weights
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-15
    Javier Duoandikoetxea; Marcel Rosenthal

    We define a scale of weighted Morrey spaces which contains different versions of weighted spaces appearing in the literature. This allows us to obtain weighted estimates for operators in a unified way. In general, we obtain results for weights of the form |x|αw(x) with w∈Ap and nonnegative α. We study particularly some properties of power-weighted spaces and in the case of the Hardy-Littlewood maximal

    更新日期:2020-06-23
  • Uniqueness of solutions to Lp-Christoffel-Minkowski problem for p < 1
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    Li Chen

    Lp-Christoffel-Minkowski problem arises naturally in the Lp-Brunn-Minkowski theory. It connects both curvature measures and area measures of convex bodies and is a fundamental problem in convex geometric analysis. Since the lack of Firey's extension of Brunn-Minkowski inequality and constant rank theorem for p<1, the existence and uniqueness of Lp-Brunn-Minkowski problem are difficult problems. In

    更新日期:2020-06-23
  • Sobolev-Type Inequalities for Dunkl Operators
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    Andrei Velicu

    In this paper we study the Sobolev inequality in the Dunkl setting using two new approaches which provide a simpler elementary proof of the classical case p=2, as well as an extension to the coefficient p=1 that was previously unknown. We also find estimates of the sharp constants for the Sobolev inequality for Dunkl gradient. Related inequalities and some improvements are also considered (Nash inequality

    更新日期:2020-06-17
  • The Cuntz–Toeplitz algebras have nuclear dimension one
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    Philip Easo; Esperanza Garijo; Sarunas Kaubrys; David Nkansah; Martin Vrabec; David Watt; Cameron Wilson; Christian Bönicke; Samuel Evington; Marzieh Forough; Sergio Girón Pacheco; Nicholas Seaton; Stuart White; Michael F. Whittaker; Joachim Zacharias

    We prove that unital extensions of Kirchberg algebras by separable stable AF algebras have nuclear dimension one. The title follows.

    更新日期:2020-06-17
  • Extrapolation of the Dirichlet problem for elliptic equations with complex coefficients
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    Martin Dindoš; Jill Pipher

    In this paper, we prove an extrapolation result for complex coefficient divergence form operators that satisfy a strong ellipticity condition known as p-ellipticity. Specifically, let Ω be a chord-arc domain in Rn and the operator L=∂i(Aij(x)∂j)+Bi(x)∂i be elliptic, with |Bi(x)|≤Kδ(x)−1 for a small K. Let p0=sup⁡{p>1:Aisp-elliptic}. We establish that if the Lq Dirichlet problem is solvable for L for

    更新日期:2020-06-17
  • Self-improvement of weighted pointwise inequalities on open sets
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    Sylvester Eriksson-Bique; Juha Lehrbäck; Antti V. Vähäkangas

    We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of p-Poincaré and p-Hardy weights for an open set Ω⊂X, where X is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection

    更新日期:2020-06-17
  • On invertible elements in reduced C⁎-algebras of acylindrically hyperbolic groups
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    M. Gerasimova; D. Osin

    Let G be an acylindrically hyperbolic group. We prove that if G has no non-trivial finite normal subgroups, then the set of invertible elements is dense in the reduced C⁎-algebra of G. The same result is obtained for finite direct products of acylindrically hyperbolic groups.

    更新日期:2020-06-17
  • Estimating Dixmier traces of Hankel operators in Lorentz ideals
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-17
    Magnus Goffeng; Alexandr Usachev

    In this paper we study Dixmier traces of powers of Hankel operators in Lorentz ideals. We extend results of Engliš-Zhang to the case of powers p≥1 and general Lorentz ideals starting from abstract extrapolation results of Gayral-Sukochev. In the special case p=2,4,6 we give an exact formula for the Dixmier trace. For general p, we give upper and lower bounds on the Dixmier trace. We also construct

    更新日期:2020-06-17
  • Regularity of the centered fractional maximal function on radial functions
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-15
    David Beltran; José Madrid

    We study the regularity properties of the centered fractional maximal function Mβ. More precisely, we prove that the map f↦|∇Mβf| is bounded and continuous from W1,1(Rd) to Lq(Rd) in the endpoint case q=d/(d−β) if f is a radial function. For d=1, the radiality assumption can be removed. This corresponds to the counterparts of known results for the non-centered fractional maximal function. The main

    更新日期:2020-06-15
  • Approximation of the average of some random matrices
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-15
    Grigory Ivanov; Márton Naszódi; Alexandr Polyanskii

    Rudelson's theorem states that if for a set of unit vectors ui and positive weights ci, we have that ∑ciui⊗ui is the identity operator I on Rd, then the sum of a random sample of Cdln⁡d of these diadic products is close to I. The ln⁡d term cannot be removed. On the other hand, the recent fundamental result of Batson, Spielman and Srivastava and its improvement by Marcus, Spielman and Srivastava show

    更新日期:2020-06-15
  • Schur multipliers of Schatten–von Neumann classes Sp
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-05
    A.B. Aleksandrov; V.V. Peller

    We study in this paper properties of Schur multipliers of Schatten von Neumann classes Sp. We prove that for p≤1, Schur multipliers of Sp are necessarily completely bounded. We also introduce for p≤1 a scale Wp of tensor products of ℓ∞ and prove that matrices in Wp are Schur multipliers of Sp. We compare this sufficient condition with the sufficient condition of membership in the p-tensor product of

    更新日期:2020-06-05
  • The triangle averaging operator
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Eyvindur A. Palsson; Sean R. Sovine

    We examine the averaging operator T corresponding to the manifold in R2d of pairs of points (u,v) satisfying |u|=|v|=|u−v|=1, so that {0,u,v} is the set of vertices of an equilateral triangle. We establish Lp×Lq→Lr boundedness for T for (1/p,1/q,1/r) in the convex hull of the set of points {(0,0,0),(1,0,1),(0,1,1),(1/pd,1/pd,2/pd)}, where pd=5d3d−2.

    更新日期:2020-06-02
  • Calderón-Zygmund estimates for generalized double phase problems
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Sumiya Baasandorj; Sun-Sig Byun; Jehan Oh

    We prove Calderón-Zygmund type estimates for distributional solutions to non-uniformly elliptic equations of generalized double phase type in divergence form. In particular, we provide sharp conditions on the nonlinear operators to establish the Calderón-Zygmund type estimates.

    更新日期:2020-06-02
  • Construction of a solution for the two-component radial Gross-Pitaevskii system with a large coupling parameter
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Jean-Baptiste Casteras; Christos Sourdis

    We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions that remain uniformly bounded are known to converge to a segregated limiting profile, with the difference of its components satisfying a limit scalar PDE. In the case of radial symmetry, under natural non-degeneracy assumptions

    更新日期:2020-06-02
  • Injectivity almost everywhere for weak limits of Sobolev homeomorphisms
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Ondřej Bouchala; Stanislav Hencl; Anastasia Molchanova

    Let Ω⊂Rn be an open set and let f∈W1,p(Ω,Rn) be a weak (sequential) limit of Sobolev homeomorphisms. Then f is injective almost everywhere for p>n−1 both in the image and in the domain. For p≤n−1 we construct a strong limit of homeomorphisms such that the preimage of a point is a continuum for every point in a set of positive measure in the image and the topological image of a point is a continuum

    更新日期:2020-06-02
  • Geometric Hardy's inequalities with general distance functions
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Nguyen Lam; Guozhen Lu; Lu Zhang

    We establish in this paper general geometric Hardy's identities and inequalities on domains in RN in the spirit of their celebrated works by Brezis-Vázquez and Brezis-Marcus. Hardy's identities are powerful tools in establishing more precise and significantly stronger inequalities than those Hardy's inequalities in the literature. More precisely, we use the notion of Bessel pairs introduced by Ghoussoub

    更新日期:2020-06-02
  • Random conductance models with stable-like jumps: Heat kernel estimates and Harnack inequalities
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Xin Chen; Takashi Kumagai; Jian Wang

    We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of the well known two-sided Gaussian heat kernel estimates by M.T. Barlow for nearest neighbor (short range) random walks on the supercritical percolation cluster. Unlike the cases of nearest neighbor conductance

    更新日期:2020-06-02
  • Strong law of large numbers for the L1-Karcher mean
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Yongdo Lim; Miklós Pálfia

    Sturm's strong law of large numbers in CAT(0) spaces has been an influential tool to study the geometric mean or also called Karcher barycenter of positive definite matrices. It provides an easily computable stochastic approximation based on inductive means. Convergence of a deterministic version of this approximation has been proved by Holbrook, providing his “nodice” theorem for the Karcher mean

    更新日期:2020-06-02
  • Multilinear operator-valued Calderón-Zygmund theory
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Francesco Di Plinio; Kangwei Li; Henri Martikainen; Emil Vuorinen

    We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness condition naturally arising in operator-valued theory. We proceed by establishing a suitable representation of multilinear, operator-valued singular integrals in terms of operator-valued

    更新日期:2020-06-02
  • Stability analysis for semilinear parabolic problems in general unbounded domains
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Luca Rossi

    We introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain, under boundary condition of the oblique derivative type. We employ these notions in the stability analysis of semilinear problems. Some of the properties we derive are new even in the Dirichlet or in the whole space cases. As an application, we show the validity of the hair-trigger

    更新日期:2020-06-02
  • A last theorem of Kalton and finiteness of Connes' integral
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    S. Lord; F. Sukochev; D. Zanin

    We connect finiteness of the noncommutative integral in Alain Connes' noncommutative geometry with the study of tensor multipliers from classical Banach space theory. For the Lorentz function spaceΛ1(Rd)={f∈L0(Rd):∫0∞μ(s,f)(1+log+⁡(s−1))ds<∞} where μ(s,f), s>0, denotes the decreasing rearrangement of f, and log+ denotes the positive part of log on (0,∞), we prove using tensor multipliers the formu

    更新日期:2020-06-02
  • Fine boundary regularity for the degenerate fractional p-Laplacian
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-02
    Antonio Iannizzotto; Sunra J.N. Mosconi; Marco Squassina

    We consider a nonlocal equation driven by the fractional p-Laplacian (−Δ)ps with s∈]0,1[ and p⩾2 (degenerate case), with a bounded reaction f and Dirichlet type conditions in a smooth domain Ω. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution u of such equation exhibits a weighted Hölder regularity up to the boundary, that is, u/dΩs∈Cα(Ω‾)

    更新日期:2020-06-02
  • Correspondence theory on p-Fock spaces with applications to Toeplitz algebras
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Robert Fulsche

    We prove several results concerning the theory of Toeplitz algebras over p-Fock spaces using a correspondence theory of translation invariant symbol and operator spaces. The most notable results are: The full Toeplitz algebra is the norm closure of all Toeplitz operators with bounded uniformly continuous symbols. This generalizes a result obtained by J. Xia [25] in the case p=2, which was proven by

    更新日期:2020-06-01
  • Instability of solutions to the Ginzburg–Landau equation on Sn and CPn
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Da Rong Cheng

    We study critical points of the Ginzburg–Landau (GL) functional and the abelian Yang–Mills–Higgs (YMH) functional on the sphere and the complex projective space, both equipped with the standard metrics. For the GL functional we prove that on Sn with n≥2 and CPn with n≥1, stable critical points must be constants. In addition, for GL critical points on Sn for n≥3 we obtain a lower bound on the Morse

    更新日期:2020-06-01
  • On the extendability by continuity of angular valuations on polytopes
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Thomas Wannerer

    A classical theorem of P. McMullen describes all valuations on polytopes that are invariant under translations and weakly continuous, i.e., continuous with respect to parallel displacements of the facets of a polytope. While it is typically not difficult to check that a valuation is weakly continuous, it is not clear how to decide whether it admits a continuous extension to convex bodies. In a special

    更新日期:2020-06-01
  • Closed ideals of operators on the Tsirelson and Schreier spaces
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Kevin Beanland; Tomasz Kania; Niels Jakob Laustsen

    Let B(X) denote the Banach algebra of bounded operators on X, where X is either Tsirelson's Banach space or the Schreier space of order n for some n∈N. We show that the lattice of closed ideals of B(X) has a very rich structure; in particular B(X) contains at least continuum many maximal ideals. Our approach is to study the closed ideals generated by the basis projections. Indeed, the unit vector basis

    更新日期:2020-06-01
  • On the upper semicontinuity of a quasiconcave functional
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Luigi De Rosa; Denis Serre; Riccardo Tione

    In the recent paper [21], the second author proved a divergence-quasiconcavity inequality for the following functional D(A)=∫Tndet⁡(A(x))1n−1dx defined on the space of positive definite matrices in Lp(Tn,Sym+(n)) with zero divergence. We consider the space Xp of tensor-fields in Lp(Tn,Sym+(n)) whose divergence is a Radon measure. We endow Xp with the weak topology given by the weak convergence in Lp

    更新日期:2020-06-01
  • Planck-scale number of nodal domains for toral eigenfunctions
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Andrea Sartori

    We study the number of nodal domains in balls shrinking slightly above the Planck scale for “generic” toral eigenfunctions. We prove that, up to the natural scaling, the nodal domains count obeys the same asymptotic law as the global number of nodal domains. The proof, on one hand, uses new arithmetic information to refine Bourgain's de-randomisation technique at Planck scale. And on the other hand

    更新日期:2020-06-01
  • Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Aris Daniilidis; Jesus A. Jaramillo; Francisco Venegas M.

    The convex cone SCSLip1(X) of real-valued smooth semi-Lipschitz functions on a Finsler manifold X is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of X. In this work we show that the subset of smooth semi-Lipschitz functions of constant strictly less than 1, denoted SC1−1(X), can be used to classify Finsler manifolds and to characterize almost isometries

    更新日期:2020-06-01
  • On densely isomorphic normed spaces
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-06-01
    Petr Hájek; Tommaso Russo

    In the first part of our note we prove that every Weakly Lindelöf Determined (WLD) (in particular, every reflexive) non-separable Banach X space contains two dense linear subspaces Y and Z that are not densely isomorphic. This means that there are no further dense linear subspaces Y0 and Z0 of Y and Z which are linearly isomorphic. Our main result (Theorem B) concerns the existence of biorthogonal

    更新日期:2020-06-01
  • Fluctuation scaling limits for positive recurrent jumping-in diffusions with small jumps
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-25
    Kosuke Yamato; Kouji Yano

    For positive recurrent jumping-in diffusions with small jumps, we establish distributional limits of the fluctuations of inverse local times and occupation times on the half line. For this purpose, we introduce and utilize eigenfunctions with modified Neumann boundary condition and apply the Krein-Kotani correspondence.

    更新日期:2020-05-25
  • Estimates for Taylor coefficients of Cauchy transforms of some Hausdorff Measures (II)
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-25
    Hong-Guang Li; Xin-Han Dong; Peng-Fei Zhang

    Let q be even, F be the Cauchy transform of the self-similar measure μ=1q∑j=0q−1μ∘Sj where Sj(z)=e2jπi/q+ρ(z−e2jπi/q) with ρ∈(0,1), and K be the attractor of {Sj}j=0q−1 and Rq=dist(0,K). As a follow-up of [8], we not only study the asymptotic formula for the Taylor coefficients {bqk−1}k=1∞ of F in |z|

    更新日期:2020-05-25
  • Estimates for Taylor coefficients of Cauchy transforms of some Hausdorff measures (I)
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-25
    Hong-Ping Li; Xin-Han Dong; Peng-Fei Zhang; Hai-Hua Wu

    Suppose that q=2m+1≥5. Let F be the Cauchy transform of the self-similar measure μ=1q∑j=0q−1μ∘Sj where Sj(z)=e2jπi/q+ρ(z−e2jπi/q) with ρ∈(0,1). Let K be the attractor of {Sj}j=0q−1 and Rq=dist(0,K). The Laurent coefficients of F in |z|>1 was studied in [18] and [2]. In this paper, we study the asymptotic formula of the Taylor coefficients {bqk−1}k=1∞ of F in |z|

    更新日期:2020-05-25
  • Off-diagonal estimates for the first order commutators in higher dimensions
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-23
    Yaryong Heo; Sunggeum Hong; Chan Woo Yang

    In this paper we study natural generalizations of the first order Calderón commutator in higher dimensions d≥2. We study the bilinear operator Tm which is given byTm(f,g)(x):=∬R2d[∫01m(ξ+tη)dt]fˆ(ξ)gˆ(η)e2πix⋅(ξ+η)dξdη. Our results are obtained under two different conditions of the multiplier m. The first result is that when K∈S′∩Lloc1(Rd∖{0}) is a regular Calderón-Zygmund convolution kernel of regularity

    更新日期:2020-05-23
  • Fractional Sobolev spaces from a complex analytic viewpoint
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-21
    Xiao Yao; Zhenqiu Zhang

    For any non-zero function u in the Schwartz space S(Rn), we prove that s↦[u]s,22 can be extended to C as a transcendental meromorphic function, which establishes a connection between the Bourgain-Brezis-Mironescu's formula, Maz'ya-Shaponshikova's formula and the residues of the transcendental meromorphic function of s↦[u]s,22 at s=0 and s=1 separately. Moreover, we study the function properties of

    更新日期:2020-05-21
  • Bilinear operator multipliers into the trace class
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-20
    Christian Le Merdy; Ivan G. Todorov; Lyudmila Turowska

    Given Hilbert spaces H1,H2,H3, we consider bilinear maps defined on the cartesian product S2(H2,H3)×S2(H1,H2) of spaces of Hilbert-Schmidt operators and valued in either the space B(H1,H3) of bounded operators, or in the space S1(H1,H3) of trace class operators. We introduce modular properties of such maps with respect to the commutants of von Neumann algebras Mi⊂B(Hi), i=1,2,3, as well as an appropriate

    更新日期:2020-05-20
  • Quantum majorization on semi-finite von Neumann algebras
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-20
    Priyanga Ganesan; Li Gao; Satish K. Pandey; Sarah Plosker

    We extend Gour et al.'s characterization of quantum majorization via conditional min-entropy to the context of semi-finite von Neumann algebras. Our method relies on a connection between conditional min-entropy and the operator space projective tensor norm for injective von Neumann algebras. We then use this approach to generalize the tracial Hahn-Banach theorem of Helton, Klep and McCullough to vector-valued

    更新日期:2020-05-20
  • Asymptotic behavior of orthogonal polynomials without the Carleman condition
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-20
    D.R. Yafaev

    Our goal is to find an asymptotic behavior as n→∞ of orthogonal polynomials Pn(z) defined by the Jacobi recurrence coefficients an,bn. We suppose that the off-diagonal coefficients an grow so rapidly that the series ∑an−1 converges, that is, the Carleman condition is violated. With respect to diagonal coefficients bn we assume that −bn(anan−1)−1/2→2β∞ for some β∞≠±1. The asymptotic formulas obtained

    更新日期:2020-05-20
  • Regularity for Dirac-harmonic maps into certain pseudo-Riemannian manifolds
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-19
    Wanjun Ai; Miaomiao Zhu

    We show the smoothness of weakly Dirac-harmonic maps from a closed spin Riemann surface into stationary Lorentzian manifolds, and obtain a regularity theorem for a class of critical elliptic systems without anti-symmetry structures.

    更新日期:2020-05-19
  • Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-19
    Cheng-Jie Liu; Dehua Wang; Feng Xie; Tong Yang

    In this paper, we are concerned with the magnetic effect on the Sobolev solvability of boundary layer equations for the 2D incompressible MHD system without resistivity. The MHD boundary layer is described by the Prandtl type equations derived from the incompressible viscous MHD system without resistivity under the no-slip boundary condition on the velocity. Assuming that the initial tangential magnetic

    更新日期:2020-05-19
  • Sobolev embedding for M1,p spaces is equivalent to a lower bound of the measure
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-19
    Ryan Alvarado; Przemysław Górka; Piotr Hajłasz

    It has been known since 1996 that a lower bound for the measure, μ(B(x,r))≥brs, implies Sobolev embedding theorems for Sobolev spaces M1,p defined on metric-measure spaces. We prove that, in fact Sobolev embeddings for M1,p spaces are equivalent to the lower bound of the measure.

    更新日期:2020-05-19
  • Blow up at infinity in the SU(3) Chern-Simons model, part I
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-19
    Ting-Jung Kuo; Youngae Lee; Chang-Shou Lin

    We consider non-topological solutions of a nonlinear elliptic system problem (see (1.4) below) derived from the SU(3) Chern-Simons models in R2. The existence of non-topological solutions even for radial symmetric case has been a long standing open problem. Recently, Choe, Kim, and Lin in [7], [8] showed the existence of radial symmetric non-topological solution when the vortex points collapse. However

    更新日期:2020-05-19
  • Absolutely continuous spectrum of multifrequency quasiperiodic Schrödinger operator
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-18
    Xuanji Hou; Jing Wang; Qi Zhou

    In this paper, we prove that for any d-frequency analytic quasiperiodic Schrödinger operator, if the frequency is weak Liouvillean, and the potential is small enough, then the corresponding operator has absolutely continuous spectrum. Moreover, in the case d=2, we even establish the existence of ac spectrum under small potential and some super-Liouvillean frequency, and this result is optimal due to

    更新日期:2020-05-18
  • Spectral rigidity for addition of random matrices at the regular edge
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-14
    Zhigang Bao; László Erdős; Kevin Schnelli

    We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues

    更新日期:2020-05-14
  • A non-linear adiabatic theorem for the one-dimensional Landau–Pekar equations
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-14
    Rupert L. Frank; Zhou Gang

    We discuss a one-dimensional version of the Landau–Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear adiabatic theorem. Dispersive estimates for solutions of the Schrödinger equation with time-dependent potential are a key technical ingredient in our proof.

    更新日期:2020-05-14
  • Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-13
    Eunhee Jeong; Sanghyuk Lee

    We study the maximal estimates for the bilinear spherical average and the bilinear Bochner-Riesz operator. First, we obtain Lp×Lq→Lr estimates for the bilinear spherical maximal function on the optimal range. Thus, we settle the problem which was previously considered by Geba, Greenleaf, Iosevich, Palsson and Sawyer, later Barrionevo, Grafakos, D. He, Honzík and Oliveira, and recently Heo, Hong and

    更新日期:2020-05-13
  • Essential self-adjointness of Liouville operator for 2D Euler point vortices
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-13
    Francesco Grotto

    We analyse the 2-dimensional Euler point vortices dynamics in the Koopman-Von Neumann approach. Classical results provide well-posedness of this dynamics involving singular interactions for a finite number of vortices, on a full-measure set with respect to the volume measure dxN on the phase space, which is preserved by the measurable flow thanks to the Hamiltonian nature of the system. We identify

    更新日期:2020-05-13
  • On the length of chains in a metric space
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-13
    Mathav Murugan

    We obtain an upper bound on the minimal number of points in an ε-chain joining two points in a metric space. This generalizes a bound due to Hambly and Kumagai (1999) for the case of resistance metric on certain self-similar fractals. As an application, we deduce a condition on ε-chains introduced by Grigor'yan and Telcs (2012). This allows us to obtain sharp bounds on the heat kernel for spaces satisfying

    更新日期:2020-05-13
  • A Littlewood-Paley description of modelled distributions
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-13
    Jörg Martin; Nicolas Perkowski

    We exhibit a fundamental link between Hairer's theory of regularity structures [11] and the paracontrolled calculus of [9]. By using paraproducts we provide a Littlewood-Paley description of the spaces of modelled distributions in regularity structures that is similar to the Besov description of classical Hölder spaces.

    更新日期:2020-05-13
  • Explicit formula for Schrödinger wave operators on the half-line for potentials up to optimal decay
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-13
    Hideki Inoue

    We give an explicit formula for the wave operators for perturbations of the Dirichlet Laplacian by a potential on the half-line. The potential is assumed to decay strictly faster than the polynomial of degree minus two. The formula consists of the main term given by the scattering operator and a function of the generator of the dilation group, and a Hilbert-Schmidt remainder term. Our method is based

    更新日期:2020-05-13
  • On the geometry of semiclassical limits on Dirichlet spaces
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-13
    Batu Güneysu

    This paper is a contribution to semiclassical analysis for abstract Schrödinger type operators on locally compact spaces: Let X be a metrizable separable locally compact space, let μ be a Radon measure on X with a full support. Let (t,x,y)↦p(t,x,y) be a strictly positive pointwise consistent μ-heat kernel, and assume that the generator Hp≥0 of the corresponding self-adjoint contraction semigroup in

    更新日期:2020-05-13
  • Super Ricci flows for weighted graphs
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-07
    Matthias Erbar; Eva Kopfer

    We present a notion of super Ricci flow for time-dependent finite weighted graphs. A challenging feature is that these flows typically encounter singularities where the underlying graph structure changes. Our notion is robust enough to allow the flow to continue past these singularities. As a crucial tool for this purpose we study the heat flow on such singular time-dependent weighted graphs with changing

    更新日期:2020-05-07
  • Cartan subalgebras for non-principal twisted groupoid C⁎-algebras
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-07
    A. Duwenig; E. Gillaspy; R. Norton; S. Reznikoff; S. Wright

    Renault proved in 2008 [22, Theorem 5.2] that if G is a topologically principal groupoid, then C0(G(0)) is a Cartan subalgebra in Cr⁎(G,Σ) for any twist Σ over G. However, there are many groupoids which are not topologically principal, yet their (twisted) C⁎-algebras admit Cartan subalgebras. This paper gives a dynamical description of a class of such Cartan subalgebras, by identifying conditions on

    更新日期:2020-05-07
  • The inverse approach to Dirac-type systems based on the A-function concept
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-06
    Fritz Gesztesy; Alexander Sakhnovich

    The principal objective in this paper is a new inverse approach to general Dirac-type systems of the formy′(x,z)=i(zJ+JV(x))y(x,z)(x≥0), where y=(y1,…,ym)⊤ and (for m1,m2∈N)J=[Im10m1×m20m2×m1−Im2],V=[0m1vv⁎0m2],m1+m2=:m, for v∈[C1([0,∞))]m1×m2, modeled after B. Simon's 1999 inverse approach to half-line Schrödinger operators. In particular, we derive the A-equation associated to this Dirac-type system

    更新日期:2020-05-06
  • Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-06
    Kamil Kaleta; René L. Schilling

    We study the long-time asymptotic behaviour of semigroups generated by non-local Schrödinger operators of the form H=−L+V; the free operator L is the generator of a symmetric Lévy process in Rd, d>1 (with non-degenerate jump measure) and V is a sufficiently regular confining potential. We establish sharp two-sided estimates of the corresponding heat kernels for large times and identify a new general

    更新日期:2020-05-06
  • Which de Branges-Rovnyak spaces have complete Nevanlinna-Pick property?
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-06
    Cheng Chu

    We characterize the de Branges-Rovnyak spaces with complete Nevanlinna-Pick property. Our method relies on the general theory of reproducing kernel Hilbert spaces.

    更新日期:2020-05-06
  • Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-06
    Nicola Soave

    We study existence and properties of ground states for the nonlinear Schrödinger equation with combined power nonlinearities−Δu=λu+μ|u|q−2u+|u|2⁎−2uin RN, N≥3, having prescribed mass∫RN|u|2=a2, in the Sobolev critical case. For a L2-subcritical, L2-critical, of L2-supercritical perturbation μ|u|q−2u we prove several existence/non-existence and stability/instability results. This study can be considered

    更新日期:2020-05-06
  • A basis of Rn with good isometric properties and some applications to denseness of norm attaining operators
    J. Funct. Anal. (IF 1.496) Pub Date : 2020-05-05
    María D. Acosta; José L. Dávila

    We characterize real Banach spaces Y such that the pair (ℓ∞n,Y) has the Bishop-Phelps-Bollobás property for operators. To this purpose it is essential using an appropriate basis of the domain space Rn. As a consequence of the mentioned characterization, we provide examples of spaces Y satisfying such property. For instance, finite-dimensional spaces, uniformly convex spaces, uniform algebras and L1(μ)

    更新日期:2020-05-05
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