Maximal functions, Littlewood-Paley theory, Riesz Transforms and Atomic Decomposition in the multi-parameter flag setting
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Bibliographic Information
Maximal functions, Littlewood-Paley theory, Riesz Transforms and Atomic Decomposition in the multi-parameter flag setting
（Memoirs of the American Mathematical Society, no. 1373）
American Mathematical Society, c2022
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Note
"September 2022, volume 279, number 1373 (second of 6 numbers)"
Includes bibliographical references (p. 101-102)
Description and Table of Contents
Description
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 Calderon reproducing formulae in the flag setting and a version of the Plancherel-Polya 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.
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