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

Michael G. Cowling*, Zhijie Fan, Ji Li, Lixin Yan

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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 H1 by square functions and by atomic decompositions, proof of the duality of H1 with BMO, and description of many interpolation spaces.
Until now, however, two aspects of the classical theory have been conspicuously absent: the characterisation of H1 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 in Chen et al. (Flag Hardy space theory on Heisenberg groups and applications. arXiv:2102.07371, 2021) on the Heisenberg group with flag structure.
Original languageEnglish
Title of host publicationThe Mathematical heritage of guido weiss
EditorsEugenio Hernández, Marco Maria Peloso, Fulvio Ricci, Fernando Sori, Anita Tabacco
Place of PublicationCham
PublisherBirkhäuser
Chapter9
Pages193-227
Number of pages35
ISBN (Electronic)9783031767937
ISBN (Print)9783031767920
DOIs
Publication statusPublished - 2025

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

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