Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting

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 a...

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Bibliographische Detailangaben
Hauptverfasser: Han, Yongsheng, Lee, Ming-Yi, Li, Ji, Wick, Brett D.
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2022
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Hardy spaces
Littlewood-Paley theory
Maximal functions
flag Hardy space
flag Riesz transforms
maximal function
Littlewood–Paley square function
atomic decomposition
Lusin area integral
ISBN:1470453452, 9781470453459
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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 decomposition in the multi-parameter flag setting. The novel ingredients in this paper include (1) establishing appropriate discrete Calderón reproducing formulae in the flag setting and a version of the Plancherel–Pólya 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 decomposition 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.
Bibliographie:September 2022, volume 279, number 1373 (second of 6 numbers)
Includes bibliographical references (p. 101-102)
ISBN:1470453452
9781470453459
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1373