Related papers: Extremely weak interpolation in $H^{\infty}$

Given an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\bar z\bar{H^p}$ be the associated star-invariant subspace of the Hardy space $H^p$. Also, we put $K_{*\theta}:=K^2_\theta\cap{\rm BMO}$. Assuming that…

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…

We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…

We study the interpolation sets for the Hardy-Sobolev spaces defined on the unit ball of ${\bf C}^n$. We begin by giving a natural extension to ${\bf C}^n$ of the condition that is known to be necessay and sufficient for interpolation sets…

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…

We study almost sure separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0-1 Komolgorov law for a sequence to be interpolating almost surely for all the…

We denote by $\Hp$ the Hilbert space of ordinary Dirichlet series with square-summable coefficients. The main result is that a bounded sequence of points in the half-plane $\sigma >1/2$ is an interpolating sequence for $\Hp$ if and only if…

We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…

Let $X$ and $M$ be a topological space and metric space, respectively. If $C(X,M)$ denotes the set of all continuous functions from X to M, we say that a subset $Y$ of $X$ is an \emph{$M$-interpolation set} if given any function $g\in M^Y$…

In [1], Y. Belov, K. Seip, and the author studied the Carleson measures for certain spaces of analytic functions of which the de Branges spaces and the model subspaces of the Hardy space H2 are the prime examples. In this paper, we continue…

Let $\mathcal H$ be the Drury-Arveson or Dirichlet space of the unit ball of $\mathbb C^d$. The weak product $\mathcal H\odot\mathcal H$ of $\mathcal H$ is the collection of all functions $h$ that can be written as $h=\sum_{n=1}^\infty f_n…

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…

Let $E$ be a subset of the unit disc $U$ of the complex plane $\CC$. Recall that $H^p(U)$ is the space of all holomorphic functions $g$ on $U$ for which $\|g\|_{H^p}$ $<$ $\infty$. Put \begin{equation} C_p(\epsilon, R) = \sup \{\sup_{|z|…

The interpolation property of Ces{\`a}ro sequence and function spaces is investigated. It is shown that $Ces_p(I)$ is an interpolation space between $Ces_{p_0}(I)$ and $Ces_{p_1}(I)$ for $1 < p_0 < p_1 \leq \infty$ and $1/p = (1 -…

We obtain a new square function characterization of the weak Hardy space $H^{p,\infty}$ for all $p\in(0,\iy)$. This space consists of all tempered distributions whose smooth maximal function lies in weak $L^p$. Our proof is based on…

We consider the Carleson embeddings of the classical Hardy spaces (on the disk) into a L p ($\mu$) space, where $\mu$ is a Carleson measure on the unit disk. This includes the case of composition operators. We characterize such operators…

The classical embedding theorem of Carleson deals with finite positive Borel measures $\mu$ on the closed unit disk for which there exists a positive constant $c$ such that $|f|_{L^2(\mu)} \leq c |f|_{H^2}$ for all $f \in H^2$, the Hardy…

In this work we study Hardy Sobolev spaces in the ball of $C^n$ with respect to interpolating sequences and Carleson measures. We compare them with the classical Hardy spaces of the ball and we stress analogies and differences.

Let $\mathcal{M}$ be a semifinite von Nemann algebra equipped with an increasing filtration $(\mathcal{M}_n)_{n\geq 1}$ of (semifinite) von Neumann subalgebras of $\mathcal{M}$. For $0<p <\infty$, let $\mathsf{h}_p^c(\mathcal{M})$ denote…

Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…