On $l^p$ -multipliers of functions analytic in the disk

TL;DR

This paper investigates bounded analytic functions in specific domains with Littlewood--Paley property, demonstrating that these functions serve as $l^p$-multipliers, thus linking domain properties to multiplier behavior.

Contribution

It establishes that bounded analytic functions in domains with Littlewood--Paley property are $l^p$-multipliers, providing a new connection between domain geometry and multiplier theory.

Findings

Bounded analytic functions in Littlewood--Paley domains are $l^p$-multipliers.

The result applies to functions in domains generated by sets with Littlewood--Paley property.

The paper advances understanding of multiplier behavior in complex analysis.

Abstract

We consider bounded analytic functions in domains generated by sets that have Littlewood--Paley property. We show that each such function is an $l^p$ -multiplier.