Maximal Functions, Littlewood-Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting - Yongsheng Han, Ming-Yi Lee, Ji Li, Brett Wick

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

Buch | Softcover
102 Seiten
2022
American Mathematical Society (Verlag)
978-1-4704-5345-9 (ISBN)
103,35 inkl. MwSt
Develops 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.
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.

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.

Erscheinungsdatum
Reihe/Serie Memoirs of the American Mathematical Society
Verlagsort Providence
Sprache englisch
Maße 178 x 254 mm
Gewicht 363 g
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 1-4704-5345-2 / 1470453452
ISBN-13 978-1-4704-5345-9 / 9781470453459
Zustand Neuware
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