Characterizations of product Hardy spaces on stratified groups by singular integrals and maximal functions

2022/10/03 by Michael Cowling, Cowling, Michael G., Zhijie Fan +5 · 1 citation
Mathematics · #42B30 (primary) #43A80 #46E30 (secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2210.01265

openalex publication_date 2022/10/03 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

A large part of the theory of Hardy spaces on products of Euclidean spaces has been extended to the setting of products of stratified Lie groups. This includes characterisation of Hardy spaces by square functions and by atomic decompositions, proof of the duality of Hardy spaces with BMO, and description of many interpolation spaces. Until now, however, two aspects of the classical theory have been conspicuously absent: the characterisation of Hardy spaces by singular integrals (of Christ--Geller type) or by (vertical or nontangential) maximal functions. In this paper we fill in these gaps by developing new techniques on products of stratified groups, using the ideas of Chen, Cowling, Lee, Li and Ottazzi on the Heisenberg group with flag structure.

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