In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood-Paley square function and area integral, Riesz transforms and the atomic decom-position in the multi-parameter flag setting. The novel ingredients in this paper include (1) establishing appropriate discrete Calder´on reproducing formulae in the flag setting and a version of the Plancherel-P´olya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels and flag version of harmonic functions; (3) developing an atomic decom-position via the finite speed propagation and area function in terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the multi-parameter Hardy space with the flag structure.
ISBN: | 9781470453459 |
Publication date: | 30th November 2022 |
Author: | Yongsheng Han, MingYi Lee, Ji Li, Brett D Wick |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 102 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Calculus and mathematical analysis |