Weak-star convergence in multiparameter Hardy spaces

TL;DR

This paper extends a classical theorem on weak-star convergence to the setting of multiparameter Hardy spaces, providing a broader understanding of convergence behaviors in these complex function spaces.

Contribution

It introduces a multiparameter version of Jones and Journe's theorem, advancing the theoretical framework of Hardy spaces.

Findings

Established weak-star convergence in multiparameter Hardy spaces.

Extended classical results to a more general setting.

Provided new tools for analysis in complex function spaces.

Abstract

We prove a multiparameter version of a classical theorem of Jones and Journe on weak-star convergence in the Hardy space $H^1$.