Fourier transform decay of distributions in Hardy-Morrey spaces

TL;DR

This paper establishes decay estimates for Fourier transforms in Hardy-Morrey spaces, linking pointwise estimates and cancellation conditions, and explores implications for Fourier multipliers and pseudodifferential operators.

Contribution

It introduces decay estimates for Fourier transforms in Hardy-Morrey spaces and analyzes their implications for operator continuity, a novel approach in this context.

Findings

Decay estimates for Fourier transforms in Hardy-Morrey spaces

Optimality results for Fourier multiplier continuity

Analysis of pseudodifferential operator boundedness

Abstract

In this paper we establish decay estimates for Fourier transform on Hardy-Morrey spaces and its localizable version. Our work include some aspects to these spaces linked up with pointwise Fourier estimates, in particular a natural approach on cancellation moment conditions. As application, we discuss the optimality for continuity of Fourier multipliers and pseudodifferential operators in Hardy-Morrey spaces.