Related papers: To Multidimensional Mellin Analysis: Besov spaces,…
We introduce and describe relations between Sobolev, Besov and Paley-Wiener spaces associated with three representations of the Lie group of affine transformations of the line. These representations are left and right regular…
We consider Banach spaces equipped with a set of strongly continuous bounded semigroups satisfying certain conditions. Using these semigroups we introduce an analog of a modulus of continuity and define analogs of Besov norms. A…
The goal of the paper is to consider Bernstein-Mellin subspaces in the Lebesgue-Mellin spaces and establishing for functions in these subspaces new sampling theorems and Riesz-Boas high-order interpolation formulas.
We explicitly describe all Hilbert function spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces considered over $\mathbb{R}^{n}$ or a half-space in $\mathbb{R}^{n}$ or a bounded Euclidean…
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…
We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space $\dot W^{1,p}$. The resulting spaces are identified as a special class of real interpolation spaces of…
We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…
Bessel potential spaces, introduced in the 1960s, are derived through complex interpolation between Lebesgue and Sobolev spaces, making them intermediate spaces of fractional differentiability order. Bessel potential spaces have recently…
We give a new description of classical Besov spaces in terms of a new modulus of continuity. Then a similar approach is used to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure.
The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation…
In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen. Our approach is based in the characterization of Lorentz spaces…
In this note, we study the multipliers from one model space to another. In the case when the corresponding inner functions are meromorphic, we give both necessary and sufficient conditions ensuring this set of multipliers is not trivial.…
The embedding relations between Besov-Triebel-Sobolev spaces and modulation spaces are determined explicitly. We extend the results of Sugimoto[2007]; Wang[2007] and Kobayashi[2011] to the most general cases. And we give the sharp embedding…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
We consider a family of Besov spaces of analytic type on the Shilov boundary $\mathcal{N}$ of a homogeneous Siegel domain $D$, and study their properties in relation to convolution, Fourier multipliers, and complex interpolation. In…
We introduce Besov and Triebel--Lizorkin spaces on a manifold with boundary adapted to H\"ormander vector fields, near a so-called non-characteristic point of the boundary. We prove sharp results in these spaces for the corresponding…
We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
It is a well established fact, that any projective algebraic variety is a moduli space of representations over some finite dimensional algebra. This algebra can be chosen in several ways. The counterpart in algebraic geometry is…
Motivated by a recent result which identifies in the special setting of the 2-adic group the Besov space $\dot{B}^{1,\infty}_{1}(\mathbb{Z}_2)$ with $BV(\mathbb{Z}_2)$, the space of function of bounded variation, we study in this article…