Step multipliers, Fourier step multipliers and multiplications on quasi-Banach modulation spaces

TL;DR

This paper establishes the boundedness of a broad class of multipliers, including the Hilbert transform, on quasi-Banach modulation spaces, and explores their implications for multiplications and convolutions.

Contribution

It introduces new boundedness results for multipliers on quasi-Banach modulation spaces, extending classical harmonic analysis tools to these spaces.

Findings

Boundedness of general multipliers including Hilbert transform

Boundedness results for multiplications and convolutions in quasi-Banach modulation spaces

Extension of harmonic analysis techniques to quasi-Banach settings

Abstract

We prove the boundedness of a general class of multipliers and Fourier multipliers, in particular of the Hilbert transform, on quasi-Banach modulation spaces. We also deduce boundedness for multiplications and convolutions for elements in such spaces.