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Record Nr. |
UNINA9910960743903321 |
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Autore |
Han Yongsheng |
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Titolo |
Maximal Functions, Littlewood-Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2022 |
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©2022 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (118 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.279 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Hardy spaces |
Maximal functions |
Littlewood-Paley theory |
Singular integrals |
Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- $H^p$-spaces |
Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory |
Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Cover -- Title page -- Acknowledgement -- Notation -- Chapter 1. Introduction and Statement of Main Results, Applications -- 1.1. Background and Main Results -- 1.2. Statement of Main Results -- 1.3. Strategy of Proofs of the Main Results -- 1.4. Applications and Related Open Questions -- Chapter 2. Flag Littlewood-Paley Estimate: | _{ }( )|₁, | _{ }( )|₁ and | _{ }( )|₁ -- 2.1. Discrete Calderón Reproducing Formula -- 2.2. Flag Plancherel-Pólya Type Inequalities -- 2.3. The Equivalence of | _{ }( )|₁ and | _{ }( )|₁ -- 2.4. The Estimate | _{ }( )|₁≲| _{ }( )|₁ -- Chapter 3. Estimates of Area Functions, Maximal Functions and Riesz Transforms via Flag Poisson Integral Technique -- 3.1. The Estimate | _ |
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{ }( )|₁≲| *|₁ -- 3.2. The Estimate | *|₁≲| ⁺|₁ -- 3.3. The Estimate | ⁺|₁≲∑ⱼ₌₁^{ + }∑_{ =1}^{ }| _{ , }( )|₁+| |₁ -- Chapter 4. Flag Maximal Functions: from Poisson Kernel to General Schwartz Kernels -- 4.1. The Equivalence | *|₁≈| *ᵩ( )|₁ -- 4.2. The Equivalence | ⁺|₁≈| ⁺ᵩ( )|₁ -- Chapter 5. Atomic Decompositions of Flag Hardy Spaces -- 5.1. Heat Kernel and Finite Speed Propagation -- 5.2. Atomic Decomposition for ¹_{ }(ℝⁿ×ℝ^{ }). -- 5.3. Proof of the Atomic Decomposition -- Chapter 6. Estimates of Riesz Transforms and Area Function via Atomic Decomposition -- Bibliography -- Back Cover. |
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Sommario/riassunto |
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"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"-- |
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