On multipliers of mixed-norm analytic F^{p,q} type spaces on the unit polydisk

TL;DR

This paper introduces new coefficient multiplier spaces for analytic Lizorkin-Triebel $F^{p,q}_{eta}$ type spaces on the unit polydisk, extending known results from classical Bergman spaces in the unit disk.

Contribution

It defines and characterizes new multiplier spaces for Lizorkin-Triebel type spaces on the polydisk, broadening the understanding of their structure and relationships.

Findings

New spaces of coefficient multipliers described

Extension of classical results to polydisk setting

Restrictions on parameters established

Abstract

We describe certain new spaces of coefficient multipliers of analytic Lizorkin-Triebel $F^{p,q}_{\alpha}$ type spaces in the unit polydisk with some restrictions on parameters.This extends some previously known assertions on coefficient multipliers in classical Bergman type spaces in the unit disk.