Related papers: A Note on multipliers between model spaces
This thesis is devoted to the study of multivariate (joint) spectral multipliers for systems of strongly commuting non-negative self-adjoint operators, $L=(L_1,\ldots,L_d),$ on $L^2(X,\nu),$ where $(X,\nu)$ is a measure space. By strong…
In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure
We determine multiplication and convolution topological algebras for classes of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.
Let $h_g^\infty$ be the space of harmonic functions in the unit ball that are bounded by some increasing radial function $g(r)$ with $\lim_{r\rightarrow 1} g(r)=+\infty$; these spaces are called growth spaces. We describe functions in…
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…
We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…
We study the problem of sampling with derivatives in shift-invariant spaces generated by totally-positive functions of Gaussian type or by the hyperbolic secant. We provide sharp conditions in terms of weighted Beurling densities. As a…
The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence,…
We consider bilinear multipliers that appeared as a distinguished particular case in the classification of two-dimensional bilinear Hilbert transforms by Demeter and Thiele [9]. In this note we investigate their boundedness on Sobolev…
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
Let (X,m) and (Y,n) be standard measure spaces. A function f in $L^\infty(X\times Y,m\times n)$ is called a (measurable) Schur multiplier if the map $S_f$, defined on the space of Hilbert-Schmidt operators from $L_2(X,m)$ to $L_2(Y,n)$ by…
We study embeddings between generalised Besov-Morrey spaces. Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov-Morrey spaces into the Lebesgue spaces are also considered. Our approach requires a…
On metric spaces equipped with doubling measures, we prove that a differentiability theorem holds for Lipschitz functions if and only if the space supports nontrivial (metric) derivations in the sense of Weaver that satisfy an additional…
We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces. As the proof is based on compact embeddings between the…
The Gel'fand-Shilov spaces of type S are considered as topological algebras with respect to the Moyal star product and their corresponding algebras of multipliers are defined and investigated. In contrast to the well-studied case of…
We extend the characterization of the Bourgain-Brezis-Mironescu type for maps from certain metric measure spaces to arbitrary metric spaces to a broader class of mollifiers.
In this article, using growth functions we introduce generalized matrix-weighted Besov-Triebel-Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. We first characterize these spaces, respectively, in terms of the…
The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…
In this article we characterize the boundedness and compactness of a Toeplitz-type operator on weighted Bergman spaces satisfying the so-called Bekolle-Bonami condition in terms of the Berezin transform.
We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we…