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  • Weighted norm inequalities in a bounded domain by the sparse domination method
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-05-22
    Emma-Karoliina Kurki, Antti V. Vähäkangas

    We prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight p-Poincaré inequality in such domains

    更新日期:2020-05-22
  • Lipschitz spaces adapted to Schrödinger operators and regularity properties
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-05-16
    Marta De León-Contreras, José L. Torrea

    Consider the Schrödinger operator \(\mathcal {{L}}=-\Delta +V\) in \(\mathbb {{R}}^n, n\ge 3,\) where V is a nonnegative potential satisfying a reverse Hölder condition of the type $$\begin{aligned} \left( \frac{1}{|B|}\int _B V(y)^qdy\right) ^{1/q}\le \frac{C}{|B|}\int _B V(y)dy, \, \text {{ for some }}q>n/2. \end{aligned}$$ We define \(\Lambda ^\alpha _\mathcal {{L}},\, 0<\alpha <2,\) the class of

    更新日期:2020-05-16
  • Reconstruction of compacta by finite approximations and inverse persistence
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-04-28
    Diego Mondéjar Ruiz, Manuel A. Morón

    The aim of this paper is to show how the homeomorphism and homotopy types of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the space. This recovering allows us to propose an alternative way to construct persistence modules from a point cloud.

    更新日期:2020-04-28
  • Kreiss bounded and uniformly Kreiss bounded operators
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-04-06
    A. Bonilla, V. Müller

    If T is a Kreiss bounded operator on a Banach space, then \(\Vert T^n\Vert =O(n)\). Forty years ago Shields conjectured that in Hilbert spaces, \(\Vert T^n\Vert = O(\sqrt{n})\). A negative answer to this conjecture was given by Spijker, Tracogna and Welfert in 2003. We improve their result and show that this conjecture is not true even for uniformly Kreiss bounded operators. More precisely, for every

    更新日期:2020-04-06
  • Local atomic decompositions for multidimensional Hardy spaces
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-03-28
    Edyta Kania-Strojec, Paweł Plewa, Marcin Preisner

    We consider a nonnegative self-adjoint operator L on \(L^2(X)\), where \(X\subseteq {{\mathbb {R}}}^d\). Under certain assumptions, we prove atomic characterizations of the Hardy space $$\begin{aligned} H^1(L) = \left\{ f\in L^1(X) \ : \ \left\| \sup _{t>0} \left| \exp (-tL)f \right| \right\| _{L^1(X)}<\infty \right\} . \end{aligned}$$ We state simple conditions, such that \(H^1(L)\) is characterized

    更新日期:2020-03-28
  • Regularizing effects concerning elliptic equations with a superlinear gradient term
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-03-04
    Marta Latorre, Martina Magliocca, Sergio Segura de León

    We consider the homogeneous Dirichlet problem for an elliptic equation driven by a linear operator with discontinuous coefficients and having a subquadratic gradient term. This gradient term behaves as \(g(u)|\nabla u|^q\), where \(1

    更新日期:2020-03-04
  • Chirality of real non-singular cubic fourfolds and their pure deformation classification
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-02-22
    S. Finashin, V. Kharlamov

    In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces

    更新日期:2020-02-22
  • Linear and bilinear operators and their zero-sets
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-02-20
    Damián Pinasco, Ignacio Zalduendo

    We study the extent to which several classical results relating linear or multilinear forms and their zero-sets can be generalised to linear or bilinear operators with values in \({\mathbb {R}}^n\). We find some analogues of the classical theorems, and also some restrictions.

    更新日期:2020-02-20
  • The fourth power mean of Dirichlet L -functions in $${\mathbb {F}}_q [T]$$Fq[T]
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-02-13
    Julio Cesar Andrade, Michael Yiasemides

    We prove results on moments of L-functions in the function field setting, where the moment averages are taken over primitive characters of modulus R, where R is a polynomial in \({\mathbb {F}}_{q}[T]\). We consider the behaviour as \({{\,\mathrm{deg}\,}}R \rightarrow \infty \) and the cardinality of the finite field is fixed. Specifically, we obtain an exact formula for the second moment provided that

    更新日期:2020-02-13
  • A simple characterization of H -convergence for a class of nonlocal problems
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-02-07
    José C. Bellido, Anton Evgrafov

    This is a follow-up of the paper J. Fernández-Bonder, A. Ritorto and A. Salort, H-convergence result for nonlocal elliptic-type problems via Tartar’s method, SIAM J. Math. Anal., 49 (2017), pp. 2387–2408, where the classical concept of H-convergence was extended to fractional \(p\)-Laplace type operators. In this short paper we provide an explicit characterization of this notion by demonstrating that

    更新日期:2020-02-07
  • Different notions of Sierpiński–Zygmund functions
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-02-06
    Krzysztof Chris Ciesielski, Tomasz Natkaniec

    A function \(f:{{\mathbb {R}}}\rightarrow {{\mathbb {R}}}\) is Sierpiński–Zygmund, \(f\in {{\,\mathrm{SZ}\,}}(\mathrm {C})\), provided its restriction \(f{\restriction }M\) is discontinuous for any \(M\subset {{\mathbb {R}}}\) of cardinality continuum. Often, it is slightly easier to construct a function \(f:{{\mathbb {R}}}\rightarrow {{\mathbb {R}}}\), denoted as \(f\in {{\,\mathrm{SZ}\,}}(\mathrm

    更新日期:2020-02-06
  • A note on biorthogonal systems
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2020-01-25
    Petr Hájek, Michal Johanis

    We consider the following problem (which is a generalisation of a folklore result Proposition 1 below): given a continuous linear operator \(T:X\rightarrow Y\), where Y is a Banach space with a (long) sub-symmetric basis, under which conditions can we find a continuous linear operator \(S:X\rightarrow Y\) such that \(S(B_X)\) contains the basis of Y. As a tool we also consider a non-separable version

    更新日期:2020-01-25
  • Matrix algebra of sets and variants of decomposition complexity
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-09-26
    Jerzy Dydak

    We introduce matrix algebra of subsets in metric spaces and we apply it to improve results of Yamauchi and Davila regarding Asymptotic Property C. Here is a representative result: Suppose X is an \(\infty \)-pseudo-metric space and \(n\ge 0\) is an integer. The asymptotic dimension\(\mathrm {asdim}(X)\) of X is at most n if and only if for any real number \(r > 0\) and any integer \(m\ge 1\) there

    更新日期:2019-09-26
  • Differentiability of the functions of the generalized Takagi Class
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-09-24
    Juan Ferrera, Javier Gómez Gil

    We introduce a generalization of the Takagi Class, considering an arbitrary countable dense set instead of the dyadic numbers that appear in the original Takagi function. This generalization contains many of the previous generalizations. We study the differentiation of the functions belonging to this Class, as well as the measure of the set of points of differentiability characterizing them through

    更新日期:2019-09-24
  • Eigenvalue comparisons in Steklov eigenvalue problem and some other eigenvalue estimates
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-09-23
    Yan Zhao, Chuanxi Wu, Jing Mao, Feng Du

    In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the first non-zero eigenvalue of the Wentzell eigenvalue problem of the weighted Laplacian, which can be seen as a natural generalization of the classical Steklov eigenvalue

    更新日期:2019-09-23
  • Reproducing kernel for elastic Herglotz functions
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-09-23
    T. Luque, M. C. Vilela

    We study the elastic Herglotz wave functions, which are entire solutions of the spectral Navier equation appearing in linearized elasticity theory with \(L^2\)-far-field patterns. We characterize in three-dimensions the set of these functions \({\varvec{\mathcal {W}}},\) as a closed subspace of a Hilbert space \({\varvec{\mathcal {H}}}\) of vector-valued functions such that they and their spherical

    更新日期:2019-09-23
  • Extremal bounded complete trajectories for nonautonomous reaction–diffusion equations with discontinuous forcing term
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-09-23
    Tomás Caraballo, José A. Langa, José Valero

    In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term of Heaviside type. Using this principle, we study the structure of the global attractor in both the autonomous and nonautonomous cases. In particular, in the last case we prove that the pullback attractor is confined between two special bounded complete trajectories, which play the

    更新日期:2019-09-23
  • Gleason parts for algebras of holomorphic functions in infinite dimensions
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-09-23
    Richard M. Aron, Verónica Dimant, Silvia Lassalle, Manuel Maestre

    For a complex Banach space X with open unit ball \(B_X,\) consider the Banach algebras \(\mathcal {H}^\infty (B_X)\) of bounded scalar-valued holomorphic functions and the subalgebra \(\mathcal {A}_u(B_X)\) of uniformly continuous functions on \(B_X.\) Denoting either algebra by \(\mathcal {A},\) we study the Gleason parts of the set of scalar-valued homomorphisms \(\mathcal {M}(\mathcal {A})\) on

    更新日期:2019-09-23
  • Extrapolation to Herz spaces with variable exponents and applications
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-08-21
    Kwok-Pun Ho

    This paper gives an extension of the extrapolation theory to Herz spaces with variable exponents. By using this extrapolation theory, we establish the Fefferman–Stein inequalities, the Rubio de Francia inequalities, the John–Nirenberg inequalities, the characterizations of BMO and the boundedness of the geometrical maximal operator on Herz spaces with variable exponents.

    更新日期:2019-08-21
  • Perturbation of eigenvalues of the Klein–Gordon operators
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-08-21
    Ivica Nakić, Krešimir Veselić

    We prove inclusion theorems for both spectra and essential spectra as well as two-sided bounds for isolated eigenvalues for Klein–Gordon type Hamiltonian operators. We first study operators of the form JG, where J, G are selfadjoint operators on a Hilbert space, \(J = J^* = J^{-1}\) and G is positive definite and then we apply these results to obtain bounds of the Klein–Gordon eigenvalues under the

    更新日期:2019-08-21
  • Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-08-01
    Carlos Galindo, Francisco Monserrat, Carlos-Jesús Moreno-Ávila

    We consider rational surfaces Z defined by divisorial valuations \(\nu \) of Hirzebruch surfaces. We introduce concepts of non-positivity and negativity at infinity for these valuations and prove that these concepts admit nice local and global equivalent conditions. In particular we prove that, when \(\nu \) is non-positive at infinity, the extremal rays of the cone of curves of Z can be explicitly

    更新日期:2019-08-01
  • Resolvent estimates for the magnetic Schrödinger operator in dimensions $$\ge 2$$≥2
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-07-29
    Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo

    It is well known that the resolvent of the free Schrödinger operator on weighted \(L^2\) spaces has norm decaying like \(\lambda ^{-\frac{1}{2}}\) at energy \(\lambda \). There are several works proving analogous high frequency estimates for magnetic Schrödinger operators, with large long or short range potentials, in dimensions \(n \ge 3\). We prove that the same estimates remain valid in all dimensions

    更新日期:2019-07-29
  • Triebel–Lizorkin–Morrey spaces associated to Hermite operators
    Rev. Mat. Complut. (IF 0.966) Pub Date : 2019-07-12
    Nguyen Ngoc Trong, Le Xuan Truong, Tran Tri Dung, Hanh Nguyen Vo

    The aim of this article is to establish molecular decomposition of homogeneous and inhomogeneous Triebel–Lizorkin–Morrey spaces associated to the Hermite operator \(\mathbb {H} \equiv -\Delta +|x|^2\) on the Euclidean space \(\mathbb {R}^n\). As applications of the molecular decomposition theory, we show the Triebel–Lizorkin–Morrey boundedness of Riesz potential, Bessel potential and spectral multipliers

    更新日期:2019-07-12
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