Vetenskap & teknik
Pocket
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
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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 LittlewoodPaley 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 Calderon reproducing formulae in the flag setting and a version of the PlancherelPolya 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.
- Format: Pocket/Paperback
- ISBN: 9781470453459
- Språk: Engelska
- Antal sidor: 102
- Utgivningsdatum: 2022-11-30
- Förlag: American Mathematical Society