Maximal operator in Dunkl-Fofana spaces

TL;DR

This paper extends Wiener amalgam spaces using Dunkl translation, explores their relationships with Dunkl-Lebesgue and Dunkl-Morrey spaces, and proves the boundedness of the Dunkl Hardy-Littlewood maximal function on these spaces.

Contribution

It introduces a generalization of Wiener amalgam spaces with Dunkl translation and establishes the boundedness of the Dunkl Hardy-Littlewood maximal function on these spaces.

Findings

Dunkl translation-based Wiener amalgam spaces are related to Dunkl-Lebesgue and Dunkl-Morrey spaces.

The Dunkl Hardy-Littlewood maximal function is bounded on the generalized Dunkl-Morrey spaces.

The paper provides new tools for analysis in Dunkl settings.

Abstract

We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and we give some relationship between these spaces, Dunkl-Lebesgue spaces and Dunkl-Morrey spaces. We prove that the Hardy-Litlewood maximal function associated with the Dunkl operators is bounded on these generalized Dunkl-Morrey spaces.