Related papers: Weak products of complete Pick spaces

Let $E$ be a Banach space such that $E'$ has the Radon-Nikod\'ym property. The aim of this work is to connect relative weak compactness in the $E$-valued martingale Hardy space $H^{1}(\mu,E)$ to a convex compactness criterion in a weaker…

The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for…

We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…

We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…

In this paper we present the general theory of cleft extensions for a cocommutative weak Hopf algebra $H$. For a weak left $H$-module algebra we obtain a bijective correspondence between the isomorphisms classes of $H$-cleft extensions…

The Sobolev space $H^{s}(\mathbb{R}^{d})$, where $s > d/2$, is an important function space that has many applications in various areas of research. Attributed to the inertia of a measuring instrument, it is desirable in sampling theory to…

The Dirichlet--Hardy space $\Ht$ consists of those Dirichlet series $\sum_n a_n n^{-s}$ for which $\sum_n |a_n|^2<\infty$. It is shown that the Blaschke condition in the half-plane $\operatorname{Re} s>1/2$ is a necessary and sufficient…

Let $(\mathcal{H}_k, \mathcal{H}_{\ell})$ be a pair of Hilbert function spaces with kernels $k, \ell$. In a 2005 paper, Shimorin showed that a certain factorization condition on $(k, \ell)$ yields a commutant lifting theorem for multipliers…

The Schur class, denoted by $\mathcal{S}(\mathbb{D})$, is the set of all functions analytic and bounded by one in modulus in the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$, that is \[ \mathcal{S}(\mathbb{D}) = \{\varphi…

A weighted composition operator on a reproducing kernel Hilbert space is given by a composition, followed by a multiplication. We study unitary and co-isometric weighted composition operators on unitarily invariant spaces on the Euclidean…

Let $\pi:G\to U(\mathcal H)$ be a unitary representation of a locally compact group. The braiding operator $F:\mathcal H\otimes\mathcal H\to \mathcal H\otimes\mathcal H$, which flips the components of the Hilbert tensor product $F(v\otimes…

This note characterizes multiplicative linear functionals on reproducing kernel Hilbert spaces of functions on the Euclidean unit ball in complex d-dimensional space, in terms of their action on kernel functions. The kernels considered are…

Let $({\mathcal X},d,\mu)$ be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and $H^1_{\rm at}({\mathcal X})$ be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions…

The aim of this paper is to show that the discrete maximal function $$\mathcal{M}_{h}f(x)=\sup_{N\in\mathbb{N}}\frac{1}{|\mathbf{N}_{h}\cap[1, N]|}\Big|\sum_{n\in \mathbf{N}_{h}\cap[1, N]}f(x-n)\Big|,\ \ \mbox{for $x\in\mathbb{Z}$},$$ is of…

Let us suppose that we have a right continuous Markov semigroup on $R^d$, $d\ge 1$, such that its potential kernel is given by convolution with a function $G_0=g(|\cdot|)$, where $g$ is decreasing, has a mild lower decay property at zero,…

We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal…

In this paper, certain classes of Hilbert spaces of Dirichlet series with weighted norms and their corresponding multiplier algebras will be explored. For a sequence $\{w_n\}_{n=n_0}^\infty $ of positive numbers, define \[\mathcal…

Given a countable dense subset D of an infinite-dimensional separable Hilbert space H the set of operators for which every vector in D except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology…

The Larson-Sweedler theorem says that a finite-dimensional bialgebra with a faithful integral is a Hopf algebra. The result has been generalized to finite-dimensional weak Hopf algebras by Vecserny\'es. In this paper, we show that the…

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of $\mathbb{C}.$ In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not…