An $H^1$ multiplier theorem on anisotropic spaces

TL;DR

This paper extends classical multiplier theorems to anisotropic spaces, proving new $H^1$ to $L^p$ multiplier results using adapted techniques, broadening the understanding of harmonic analysis in anisotropic contexts.

Contribution

It introduces an $H^1 ightarrow L^p$ multiplier theorem in anisotropic spaces, generalizing previous isotropic results with new methodological approaches.

Findings

Established $H^1 ightarrow L^p$ multiplier theorem for anisotropic spaces.

Extended classical $H^1$ multiplier results to anisotropic settings.

Demonstrated the applicability of existing techniques in a broader context.

Abstract

A parallel result of (the classical) Sledd--Stegenga's $H^1\rightarrow L^1$ multiplier theorem was obtained on the $H^1$ space under the anisotropic settings. Based on the same technique, an $H^1\rightarrow L^p$ multiplier theorem is also proved for $1\leq p<\infty$.