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

• Autore: Han Yongsheng
• Pubblicazione: Providence : , : American Mathematical Society, , 2022; ©2022
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (118 pages)
• Disciplina: 515/.2433; 515.2433
• Soggetto topico: 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.)
• Classificazione: 42B3042B2542B20
• Altri autori: LeeMing-Yi LiJi
• Nota di contenuto: 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 | _{ }( )|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.
• Sommario/riassunto: "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"--
• Titolo autorizzato: Maximal Functions, Littlewood-Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting
• ISBN: 9781470472276; 1470472279
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910960743903321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society