Maximal Functions, Littlewood-Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting
Seiten
2022
American Mathematical Society (Verlag)
978-1-4704-5345-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5345-9 (ISBN)
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.
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 | 03.10.2022 |
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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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Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
59,95 €