Interpolating sequences for some subsets of analytic Besov type spaces

TL;DR

This paper characterizes interpolating sequences for certain analytic Besov spaces and their multiplier classes, providing a comprehensive description under specific parameter conditions and linking to $L^p$ and Bloch space properties.

Contribution

It offers a complete description of interpolating sequences for multipliers of analytic Besov spaces and related subspaces within specified parameter ranges.

Findings

Characterization of interpolating sequences for $M(B_p(s))$ and $F(p, p-2, s) igcap H^ ^\infty$.

Connection between these sequences and $L^p$ conditions.

Analysis of the closure of $F(p, p-2, s)$ in the Bloch space.

Abstract

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 give a completed description of interpolating sequences for $M(B_p(s))$ and $F(p, p-2, s)\cap H^\infty$. We also consider certain condition appeared in this description by an $L^p$ characterization and the closure of $F(p, p-2, s)$ in the Bloch space.