We establish a sharp higher integrability near the initial boundary for a weak solution to the following p-Laplacian type system:

We make the polynomial dependence on the fixed representation π in our previous subconvex bound of L⁢(12,π⊗χ) for GL2×GL1 explicit, especially in terms of the usual conductor 𝐂⁢(πfin). There is no clue that the original choice, due to Michel and Venkatesh, of the test function at the infinite places should be the optimal one. Hence we also investigate a possible variant of such local choices in some

We study the generalised Iwasawa invariants of ℤpd-extensions of a fixed number field K. Based on an inequality between ranks of finitely generated torsion ℤp⁢[[T1,…,Td]]-modules and their corresponding elementary modules, we prove that these invariants are locally maximal with respect to a suitable topology on the set of ℤpd-extensions of K, i.e., that the generalised Iwasawa invariants of a ℤpd-extension

In 1977, Colville, Davis, and Keimel [Positive derivations on f-rings, J. Aust. Math. Soc. Ser. A 23 1977, 3, 371–375] proved that a positive derivation on an Archimedean f-algebra A has its range in the set of nilpotent elements of A. The main objective of this paper is to obtain a generalization of the above Colville, Davis and Keimel result to general derivations. Moreover, we give a new version

We prove a result that enables us to calculate the rational homotopy of a wide class of spaces by the theory of minimal models.

The Cauchy problem of the 2D Zakharov–Kuznetsov equation ∂t⁡u+∂x⁡(∂x⁢x+∂y⁢y)⁡u+u⁢ux=0 is considered. It is shown that the 2D Z-K equation is locally well-posed in the endpoint Sobolev space H-1/4, and it is globally well-posed in H-1/4 with small initial data. In this paper, we mainly establish some new dyadic bilinear estimates to obtain the results, where the main novelty is to parametrize the singularity

We study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length

The twin group Tn is a right-angled Coxeter group generated by n-1 involutions, and the pure twin group PTn is the kernel of the natural surjection from Tn onto the symmetric group on n symbols. In this paper, we investigate some structural aspects of these groups. We derive a formula for the number of conjugacy classes of involutions in Tn, which, quite interestingly, is related to the well-known

Recently, the problem of bounding the sup norms of L2-normalized cuspidal automorphic newforms ϕ on GL2 in the level aspect has received much attention. However at the moment strong upper bounds are only available if the central character χ of ϕ is not too highly ramified. In this paper, we establish a uniform upper bound in the level aspect for general χ. If the level N is a square, our result reduces

Journal Name: Forum Mathematicum Volume: 32 Issue: 5 Pages: i-iv

In this paper, we study the Lq-Lr boundedness of bi-parameter Fourier integral operators defined by general rough Hörmander class amplitudes.

We extend the theorems of [M. Greenblatt, Lp Sobolev regularity of averaging operators over hypersurfaces and the Newton polyhedron, J. Funct. Anal. 276 2019, 5, 1510–1527] on Lp to Lsp Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving Lp to Lsq boundedness results for such operators. Here q≥p but s can be positive, negative, or

We prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form

This paper concerns the study of the Schwartz differential equation {h,τ}=s⁢E4⁡(τ), where E4 is the weight 4 Eisenstein series and s is a complex parameter. In particular, we determine all the values of s for which the solutions h are modular functions for a finite index subgroup of SL2⁡(ℤ). We do so using the theory of equivariant functions on the complex upper-half plane as well as an analysis of

We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for which the nice basis is orthogonal and a more general class associated to order two permutations

In this paper, we establish an improved variable coefficient version of the square function inequality, by which the local smoothing estimate Lαp→Lp for the Fourier integral operators satisfying cinematic curvature condition is further improved. In particular, we establish almost sharp results for 2

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description

By making use of the generating function method, we derive several summation formulae involving Stirling numbers and Lah numbers as well as other classical combinatorial numbers named after Bernoulli, Euler, Bell, Genocchi, Cauchy, Derangement, Harmonic, Fibonacci and Lucas.

For any real number p∈[1,+∞), we characterise the operations ℝI→ℝ that preserve p-integrability, i.e., the operations under which, for every measure μ, the set ℒp⁢(μ) is closed. We investigate the infinitary variety of algebras whose operations are exactly such functions. It turns out that this variety coincides with the category of Dedekind σ-complete truncated Riesz spaces, where truncation is meant

This paper studies the two-weight estimates of variation and oscillation operators for commutators of singular integrals with weighted BMO functions. A new characterization of weighted BMO spaces via the boundedness of variation and oscillation operators for the iterated commutators of Calderón–Zygmund singular integrals in the two-weight setting is given.

In the present paper, we introduce a new concept of convexity which is generated by a family of endomorphisms of an Abelian group. In Abelian groups, equipped with a translation invariant metric, we define the boundedness, the norm, the modulus of injectivity and the spectral radius of endomorphisms. Beyond the investigation of their properties, our first main goal is an extension of the celebrated

We introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman–Stein-type inequalities that

A skew generalized power series ring R⁢[[S,ω,≤]] consists of all functions from a strictly ordered monoid (S,≤) to a ring R whose support is artinian and narrow, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of this ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series

In this article, we revisit Rankin–Selberg integrals established by Jacquet, Piatetski-Shapiro and Shalika. We prove the equality of Rankin–Selberg local factors defined with Schwartz–Bruhat functions and the factors attached to good sections, introduced by Piatetski-Shapiro and Rallis. Moreover, we propose a notion of exceptional poles in the framework of good sections. For cases of Rankin–Selberg

Let X be a nonsingular complex projective surface. The Weyl and Zariski chambers give two interesting decompositions of the big cone of X. Following the ideas of [T. Bauer and M. Funke, Weyl and Zariski chambers on K3 surfaces, Forum Math. 24 2012, 3, 609–625] and [S. A. Rams and T. Szemberg, When are Zariski chambers numerically determined?, Forum Math. 28 2016, 6, 1159–1166], we study these two decompositions

Journal Name: Forum Mathematicum Volume: 32 Issue: 4 Pages: i-iv

The aim of this note is to correct the proof of Proposition 2.15 in the original article [M. Doucha, Metrical universality for groups, Forum Math. 29 2017, 4, 847–872].

We prove a uniqueness type theorem for (weak, total) integrals on a Frobenius cowreath in a monoidal category. When the cowreath is, moreover, pre-Galois, we construct a Morita context relating the subalgebra of coinvariants and a certain wreath algebra. Then we see that the strictness of the Morita context is related to the Galois property of the cowreath and the existence of a weak total integral

In this paper we discuss coefficient problems for functions in the class 𝒞0⁢(k). This family is a subset of 𝒞, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate

Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article, we show that such solutions also solve a fixed point problem by exhibiting a suitable functional. Convergence then follows from consistency and stability, two notions

Classical Castelnuovo Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most (c+12) and the equality is attained if and only if the variety is of minimal degree. Also G. Fano’s generalization of Castelnuovo Lemma implies that the next case occurs if and only if the variety is a del Pezzo variety. Recently

A generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In this paper we give a characterisation of a polyhedral product ZK⁢(X,A) whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower

We deal with instanton bundles on the product ℙ1×ℙ2 and the blow up of ℙ3 along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.

We introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group H3⁢(G,C⁢(A)) with the obstructions to the existence of admissible extensions of A by G which realize the given abstract kernel. We also show that if such extensions exist, then they are classified by H2⁢(G,C⁢(A)).

Throughout this paper we show that under certain conditions the method for describing solvable Leibniz (resp. Lie) algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to the case Leibniz (resp. Lie) superalgebras. Moreover, after having established the general method for Lie and Leibniz superalgebras, we classify all the solvable superalgebras

We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective space. Natural examples of such groups of germ maps are given by holonomy groups and monodromy groups of integrable systems (foliations) under certain conditions

We show that unitary groups of II1 factors and of properly infinite von Neumann algebras have uncountable cofinality and the Bergman property. In particular, we obtain a short alternative proof for the strong uncountable cofinality of U⁢(ℓ2⁢(ℕ)), which was first proven by Ricard and Rosendal.

Let D be a division ring of fractions of a crossed product F⁢[G,η,α], where F is a skew field and G is a group with Conradian left-order ≤. For D we introduce the notion of freeness with respect to ≤ and show that D is free in this sense if and only if D can canonically be embedded into the endomorphism ring of the right F-vector space F⁢((G)) of all formal power series in G over F with respect to

In this paper we show the existence and uniqueness of strong solutions for a large class of backward SPDEs, where the coefficients satisfy a specific type Lyapunov condition instead of the classical coercivity condition. Moreover, based on the generalized variational framework, we also use the local monotonicity condition to replace the standard monotonicity condition, which is applicable to various

We show that there exists a constant a such that, for every subgroup H of a finite group G, the number of maximal subgroups of G containing H is bounded above by a|G:H|3/2. In particular, a transitive permutation group of degree n has at most a⁢n3/2 maximal systems of imprimitivity. When G is soluble, generalizing a classic result of Tim Wall, we prove a much stronger bound, that is, the number of

Let the 2×2 expanding matrix Rk be an integer Jordan matrix, i.e., Rk=diag⁡(rk,sk) or Rk=J⁢(pk), and let Dk={0,1,…,qk-1}⁢v with v=(1,1)T and 2≤qk≤pk,rk,sk for each natural number k. We show that the sequence of Hadamard triples {(Rk,Dk,Ck)} admits a spectrum of the associated Moran measure provided that lim infk→∞⁡2⁢qk⁢∥Rk-1∥<1.

Let the self-affine measure μM,D be generated by an expanding real matrix M=diag⁡(ρ1-1,ρ2-1) and an integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with α1⁢β2-α2⁢β1≠0. In this paper, the sufficient and necessary conditions for L2⁢(μM,D) to contain an infinite orthogonal set of exponential functions are given.

Baer’s Criterion for Injectivity is a useful tool of the theory of modules. Its dual version (DBC) is known to hold for all right perfect rings, but its validity for the non-right perfect ones is a complex problem (first formulated by C. Faith [Algebra. II. Ring Theory, Springer, Berlin, 1976]). Recently, it has turned out that there are two classes of non-right perfect rings: (1) those for which DBC

In this paper, we study the varieties of nilpotent Lie superalgebras of dimension ≤5. We provide the algebraic classification of these superalgebras and obtain the irreducible components in every variety. As a byproduct, we construct rigid nilpotent Lie superalgebras of arbitrary dimension.

We introduce an intrinsic filtration to the magnitude chain complex of a metric space, and study basic properties of the associated spectral sequence of the magnitude homology. As an application, the third magnitude homology of the circle is computed.

We show that any regular (right) Schreier extension of a monoid M by a monoid A induces an abstract kernel Φ:M→End⁡(A)Inn⁡(A). If an abstract kernel factors through SEnd⁡(A)Inn⁡(A), where SEnd⁡(A) is the monoid of surjective endomorphisms of A, then we associate to it an obstruction, which is an element of the third cohomology group of M with coefficients in the abelian group U⁢(Z⁢(A)) of invertible

We consider nonlinear stochastic wave equations driven by time-space white noise. The existence of solutions is proved by the method of successive approximations. Next we apply Newton’s method. The main result concerning its first-order convergence is based on Cairoli’s maximal inequalities for two-parameter martingales. Moreover, a second-order convergence in a probabilistic sense is demonstrated

The main purpose of this paper is to establish, using the bi-parameter Littlewood–Paley–Stein theory (in particular, the bi-parameter Littlewood–Paley–Stein square functions), a Calderón–Torchinsky type theorem for the following Fourier multipliers on anisotropic product Hardy spaces Hp⁢(ℝn1×ℝn2;A→) (0

We give necessary and sufficient conditions for the group of a rational maximal bifix code Z to be isomorphic with the F-group of Z∩F, when F is recurrent and Z∩F is rational. The case where F is uniformly recurrent, which is known to imply the finiteness of Z∩F, receives special attention. The proofs are done by exploring the connections with the structure of the free profinite monoid over the alphabet

We obtain approximation bounds for products of quasimodes for the Laplace–Beltrami operator on compact Riemannian manifolds of all dimensions without boundary. We approximate the products of quasimodes uv by a low-degree vector space Bn, and we prove that the size of the space dim⁡(Bn) is small. In this paper, we first study bilinear quasimode estimates of all dimensions d=2,3, d=4,5 and d≥6, respectively

Journal Name: Forum Mathematicum Volume: 32 Issue: 3 Pages: i-iv

We generalize the Alvis–Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis–Curtis duality of infinite type, which we define in this paper, also interchanges the irreducible representations in the principal representation category.

Let ℒ=-Δ𝔾+V be a Schrödinger operator on the stratified Lie group 𝔾, where Δ𝔾 is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class Bq0 with q0>𝒬/2 and 𝒬 is the homogeneous dimension of 𝔾. In this article, by Campanato type spaces Λℒα⁢(𝔾), we introduce Hardy type spaces associated with ℒ denoted by Hℒp⁢(𝔾) and prove the atomic characterization of Hℒp⁢(𝔾)

In this paper, we show that if b∈L2⁢(ℝn), then the bilinear form defined on the product of the non-homogeneous Sobolev spaces Hs2⁢(ℝn)×Hs2⁢(ℝn), 0

In this paper, we consider the long time behavior of solutions for 3D incompressible MHD equations with fractional Laplacian. Firstly, in a periodic bounded domain, we prove the existence of a global attractor. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and magnetic fields. Finally, in the whole space ℝ3, we establish the sharp algebraic

After the celebrated work of L. Hörmander on the one-parameter pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, geometric analysis, harmonic analysis, theory of several complex variables and other branches of modern analysis. For instance, they are used to construct parametrices and establish the regularity

This paper gives an explicit formula of the asymptotic expansion of the Kobayashi–Royden metric on the punctured sphere ℂ⁢ℙ1∖{0,1,∞} in terms of the exponential Bell polynomials. We prove a local quantitative version of the Little Picard’s Theorem as an application of the asymptotic expansion. Furthermore, the approach in the paper leads to the interesting consequence that the coefficients in the asymptotic

Let V,W be representations of a cyclic group G of prime order p over a field 𝕜 of characteristic p. The module of covariants 𝕜⁢[V,W]G is the set of G-equivariant polynomial maps V→W, and is a module over 𝕜⁢[V]G. We give a formula for the Noether bound β⁢(𝕜⁢[V,W]G,𝕜⁢[V]G), i.e. the minimal degree d such that 𝕜⁢[V,W]G is generated over 𝕜⁢[V]G by elements of degree at most d.

In this paper, we study the weighted sums of multiple t-values and of multiple t-star values at even arguments. Some general weighted sum formulas are given, where the weight coefficients are given by (symmetric) polynomials of the arguments.

Let G be a connected complex simple Lie group, and let G^d be the set of all equivalence classes of irreducible unitary representations with non-vanishing Dirac cohomology. We show that G^d consists of two parts: finitely many scattered representations, and finitely many strings of representations. Moreover, the strings of G^d come from L^d via cohomological induction and they are all in the good range