Related papers: Interpolating sequences for weighted Bergman space…

For $\alpha>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal B^p_\alpha$ of harmonic functions on the real hyperbolic ball and obtain an atomic decomposition of these spaces in terms of reproducing kernels. We show that an…

Let $0<p<\infty$, $\beta>-1$, and $\Omega$ be a strongly pseudoconvex bounded domain with a smooth boundary in $\mathbb{C}^n$. We will study the interpolation problem for weighted Bergman spaces $A^p_\beta(\Omega)$. In the case, $1\leq…

Let $S$ be a sequence of points in $\Omega ,$ where $\Omega$ is the unit ball or the unit polydisc in ${\mathbb{C}}^{n}.$ Denote $H^{p}$($\Omega $) the Hardy space of $\Omega .$ Suppose that $S$ is $H^{p}$ interpolating with $p\geq 2.$ Then…

Let $A$ be a sequence of points of $\mathbb{B}^n$ the unit ball in $\mathbb{C}^n.$ In terms of interpolating vectorial function (or Amar's function)[1], we give a necessary condition on $A$ to be interpolating for the weighted Bergman space…

The author showed that a sequence in the unit disk is a zero sequence for the Bergman space $A^p$ if and only if a certain weighted space $L^p(W}$ contains a nontrivial analytic function. In this paper it is shown that the sequence is an…

Carleson measures and interpolating and sampling sequences for weighted Bergman spaces on the unit disk are described for weights that are radial and grow faster than the standard weights $(1-|z|)^{-\alpha}$, $0<\alpha<1$. These results…

Title: On linear extension for interpolating sequences. Author: Eric Amar Abstract: Let A be a uniform algebra on the compact space X and $\sigma $ a probability measure on X. We define the Hardy spaces $H^{p}(\sigma)$ and the…

Let $B_p(s)$ be an analytic Besov type space. Let $M(B_p(s))$ be the class of multipliers of $B_p(s)$ and let $F(p, p-2, s)$ be the M\"obius invariant subspace generated by $B_p(s)$. In this paper, when $0<s<1$ and $\max\{s, 1-s\}<p\leq 1$,…

We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^\alpha$, to more general weights.

There has been a great deal of work done in recent years on weighted Bergman spaces $\apa$ on the unit ball $\bn$ of $\cn$, where $0<p<\infty$ and $\alpha>-1$. We extend this study in a very natural way to the case where $\alpha$ is {\em…

A sequence which is a finite union of interpolating sequences for $H^\infty$ have turned out to be especially important in the study of Bergman spaces. The Blaschke products $B(z)$ with such zero sequences have been shown to be exactly…

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the…

For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\mathbb C}^n$, we determine exactly when $A^p_\alpha\subset H^q$ or $H^p\subset A^q_\alpha$, where $0<q<\infty$, $0<p<\infty$, and $-\infty<\alpha<\infty$. For each…

This monograph is devoted to the study of the weighted Bergman space $A^p_\om$ of the unit disc $\D$ that is induced by a radial continuous weight $\om$ satisfying {equation}\label{absteq} \lim_{r\to…

We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…

The Hardy spaces of Dirichlet series denoted by ${\cal H}^p$ ($p\ge1$) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two…

We study complete interpolating sequences in two types of small Fock spaces, $\mathcal{F}^p_{\alpha +}$ and $\mathcal{F}^p_{\alpha}$, for $0 < p \le \infty$. One-sided small Fock spaces $\mathcal{F}^p_{\alpha +}$ are well-studied spaces of…

Let $\mathcal{M}$ be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace $\tau$. Let $d$ be an injective positive measurable operator with respect to $(\mathcal{M}, \tau)$ such that $d^{-1}$ is also measurable.…

In this work, we prove that if S is a dual bounded sequence in the unit ball B of C^n for the Hardy class H^p(B), then S is H^s(B) interpolating with the linear extension property.

We describe the complete interpolating sequences for the Paley-Wiener spaces $L^p_\pi$ ($1<p<\infty$) in terms of Muckenhoupt's $(A_p)$ condition. For $p=2$, this description coincides with those given by Pavlov (1979), Nikol'skii (1980),…