Related papers: Riesz-Kolmogorov type compactness criteria in func…

The class of subsets of locally convex spaces called $\mu$-compact sets is considered. This class contains all compact sets as well as several noncompact sets widely used in applications. It is shown that many results well known for compact…

We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_\omega$, for weight functions $\omega$ in the sense of Braun, Meise and…

We provide an abstract framework for a Logvinenko-Sereda type theorem, where the classical compactness assumption on the support of the Fourier transform is replaced by the assumption that the functions under consideration belong to a…

We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces $Z$. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices $s<1,$ as well as the first order…

In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit…

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The main aim of this paper is to provide necessary and sufficient…

We prove some refinements of concentration compactness principle for Sobolev space $W^{1,n}$ on a smooth compact Riemannian manifold of dimension $n$. As an application, we extend Aubin's theorem for functions on $\mathbb{S}^{n}$ with zero…

We give a general version of Bryc's theorem valid on any topological space and with any algebra $\mathcal{A}$ of real-valued continuous functions separating the points, or any well-separating class. In absence of exponential tightness, and…

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of…

We study Riesz bases/Riesz sequences of reproducing kernels in the model space $K_\theta$ in connection with the corresponding Schur--Nevanlinna parameters and functions. In particular, we construct inner functions with given…

This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…

On rank one Riemannian symmetric spaces of compact type (of dimension $\ge 2$), we first obtain a quantitative characterization of H\"older continuity in terms of Ces\`aro means. In addition to some approximation theoretic applications, we…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

We characterize boundedness and compactness of Toeplitz operators on large vector-valued Fock spaces with Dall'Ara's weights [Adv.\ Math., 285 (2015) 1706--1740] in terms of generalized Berezin transforms, averaging functions, and Carleson…

In this paper, we establish a new characterization of weighted $\rm{VMO}$ spaces, which are essential different from the classical $\rm{VMO}$ spaces, via the compactness of sparse operators, commutators of Riesz potentials and fractional…

Using Gutzmer's formula, due to Lassalle, we characterise the image of Sobolev spaces under the Segal-Bargmann transform on compact Riemannian symmetric spaces.

In this paper we discuss compactness estimates for the $\bar \partial $-Neumann problem in the setting of weighted $L^2$-spaces on $\mathbb{C}^n.$ For this purpose we use a version of the Rellich - Lemma for weighted Sobolev spaces.

Cocompactness is a useful weaker counterpart of compactness in the study of imbeddings between function spaces. In this paper we show that subcritical continuous imbeddings of fractional Sobolev spaces and Besov spaces over \mathbb{R}^{N}…

In the present paper, we study the boundedness and compactness of Toeplitz operators and Berezin-type operators between different weighted Bergman spaces over tubular domains in $\mathbb{C}^n$. We establish their connection with Carleson…

We prove a characterization for the Peetre type $K$-functional on $\mathbb{M}$, a compact two-point homogeneous space, in terms the rate of approximation of a family of multipliers operator defined to this purpose. This extends the well…