Different approach to the decomposition theory of $HM^p_{q,{\Delta_{\nu}}}$ Hardy-Morrey spaces

TL;DR

This paper introduces Hardy-Morrey spaces associated with Laplace-Bessel equations, establishing an atomic decomposition theory that parallels classical Hardy spaces, advancing the understanding of these specialized function spaces.

Contribution

It develops a new atomic decomposition framework for Hardy-Morrey spaces linked to Laplace-Bessel operators, extending classical Hardy space theory.

Findings

Defined Hardy-Morrey spaces via maximal functions

Established atomic decomposition with similar cancellation properties to classical Hardy spaces

Extended Hardy space theory to Laplace-Bessel related spaces

Abstract

The Hardy-Morrey spaces related to Laplace-Bessel differential equations are introduced in terms of maximal functions. The atomic decomposition theory which has the same cancellation properties of the $H^{p}_{\Delta_{\nu}}(\mathbb{R}^{n}_{+})$ Hardy spaces is established.