Title: Maximal Functions, Littlewood-paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting (Memoirs of the American Mathematical Society, 279)
Publisher: Amer Mathematical Society
Language: English
ISBN 10: 1470453452
ISBN 13: 9781470453459
Binding: Soft cover
Condition: New

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"In this monograph, 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 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 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"--

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