On weak-star convergence in product Hardy spaces on spaces of homogeneous type

TL;DR

This paper extends a classical weak-star convergence theorem from Hardy spaces to product spaces of homogeneous type, utilizing recent advanced tools in the field.

Contribution

It generalizes weak-star convergence results to product spaces of homogeneous type, broadening the applicability of previous theorems.

Findings

Proves weak-star convergence in product Hardy spaces on homogeneous type spaces.

Utilizes recent developments in harmonic analysis tools for the setting.

Extends classical theorems to more general geometric contexts.

Abstract

A classical theorem of Jones and Journ\'e on weak-star convergence in the Hardy space $H^1$ was generalised to the multiparameter setting by Pipher and Treil. We prove the analogous result when the underlying space is a product space of homogeneous type. The main tools we use for this setting are from recent work in papers by Chen, Li and Ward and by Han, Li and Ward.