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

Yongsheng Han (author); Ming-Yi Lee (author); Ji Li (author) & Brett Wick (author)

Softcover

ISBN 10: 1470453452 ISBN 13: 9781470453459

Publisher: American Mathematical Society, 2022

Synopsis

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.

About this title

About the Author

Yongsheng Han, Auburn University, GA.

Ming-Yi Lee, National Central University, Chung-Li, Taiwan, and National Center for Theoretical Sciences, Taipei, Taiwan.

Ji Li, Macquarie University, Sydney, Australia.

Brett Wick, Washington University, St. Louis, Missouri.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 1470453452
• ISBN 13: 9781470453459
• Binding: Paperback
• Number of pages: 102