Fefferman-Stein inequalities for the \mathbb{Z}_2^d Dunkl maximal operator

TL;DR

This paper proves Fefferman-Stein inequalities for the Dunkl maximal operator linked to reflection groups, extending the results to related operators in Dunkl analysis, thus advancing harmonic analysis in this context.

Contribution

It introduces Fefferman-Stein inequalities for the Dunkl maximal operator associated with finite reflection groups, broadening the scope of harmonic analysis tools in Dunkl's framework.

Findings

Fefferman-Stein inequalities established for Dunkl maximal operator

Results extended to a broad class of Dunkl-related operators

Advances harmonic analysis techniques in Dunkl's setting

Abstract

In this article, we establish the Fefferman-Stein inequalities for the Dunkl maximal operator associated with a finite reflection group generated by the sign changes. Similar results are also given for a large class of operators related to Dunkl's analysis.