Maximal Functions, Littlewood-paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting (Memoirs of the American Mathematical Society, 279) - Softcover

Han, Yongsheng; Lee, Ming-Yi; Li, Ji; Wick, Brett

Softcover

ISBN 10: 1470453452 ISBN 13: 9781470453459

Publisher: Amer Mathematical Society

Synopsis

"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"--

Edition details

• Publisher: Amer Mathematical Society
• Language: English
• ISBN 10: 1470453452
• ISBN 13: 9781470453459
• Binding: Paperback
• Number of pages: 102