The Hardy space H1 in the rational Dunkl setting

TL;DR

This paper explores the Hardy space H1 within the rational Dunkl setting, providing atomic and maximal function characterizations, and establishing a Fourier multiplier theorem in one-dimensional and product cases.

Contribution

It introduces atomic and heat maximal characterizations of H1 in the Dunkl setting and proves a Fourier multiplier theorem, extending harmonic analysis tools to this context.

Findings

Atomic characterization of H1 in Dunkl setting

Heat maximal operator characterization of H1

Fourier multiplier theorem for H1

Abstract

This paper consists in a first study of the Hardy space H1 in the rational Dunkl setting. Following Uchiyama's approach, we characterizee H1 atomically and by means of the heat maximal operator. We also obtain a Fourier multiplier theorem for H1. These results are proved here in the one-dimensional case and in the product case.