Fourier multipliers for Hardy spaces of Dirichlet series

TL;DR

This paper investigates Fourier multipliers in Dirichlet-Hardy spaces, establishing a Littlewood-Paley inequality that proves Dirichlet monomials form a Schauder basis for p>1, advancing the understanding of harmonic analysis in this context.

Contribution

It introduces new results on Fourier multipliers and proves a Littlewood-Paley inequality for Dirichlet-Hardy spaces, showing Dirichlet monomials form a Schauder basis for p>1.

Findings

Established a Littlewood-Paley inequality for Dirichlet-Hardy spaces

Proved Dirichlet monomials form a Schauder basis for p>1

Provided new insights into Fourier multipliers in this setting

Abstract

We obtain new results on Fourier multipliers for Dirichlet-Hardy spaces. As a consequence, we establish a Littlewood-Paley type inequality which yields a simple proof that the Dirichlet monomials form a Schauder basis for p>1.