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010 a| 2022048346;

020 a| 9781470453459q| (paperback);

020 z| 9781470472276q| (epub);

035 a| (WaSeSS)ssj0002763835;

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049 a| EREEa| NEHH;

050 00 a| QA331b| .H218 2022;

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084 a| 42B30a| 42B25a| 42B202| msc;

100 1 a| Han, Yongsheng.=| ^A351804;

245 10 a| Maximal functions, Littlewood-Paley theory, Riesz transforms and atomic decomposition in the multi-parameter flag settingh| [electronic resource] /c| Yongsheng Han, Ming-Yi Lee, Ji Li, Brett D. Wick.;

260 a| Providence, RI :b| American Mathematical Society,c| 2022.;

300 a| ix, 102 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 279, Number 1373;

504 a| Includes bibliographical references.;

505 0 a| Introduction and Statement of Main Results, Applications -- Flag Littlewood-Paley Estimate: g| F (f )1| , S| F (f )1| and S| F (U ) | -- Estimates of Area Functions, Maximal Functions and Riesz Transforms via Flag Poisson Integral Technique -- Flag Maximal Functions: from Poisson Kernel to General Schwartz Kernels -- Atomic Decompositions of Flag Hardy Spaces -- Estimates of Riesz Transforms and Area Function via Atomic Decomposition.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Hardy spaces.=| ^A78108;

650 0 a| Maximal functions.=| ^A182189;

650 0 a| Littlewood-Paley theory.=| ^A351805;

650 0 a| Singular integrals.=| ^A347316;

650 7 a| Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- $H^p$-spaces.2| msc;

650 7 a| Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory.2| msc;

650 7 a| Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.).2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Lee, Ming-Yi.?| UNAUTHORIZED;

700 1 a| Li, Jic| (Lecturer in Mathematics)?| UNAUTHORIZED;

700 1 a| Wick, Brett D.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=29731900;

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Maximal functions, Littlewood-Paley theory, Riesz transforms and atomic decomposition in the multi-parameter flag setting / Yongsheng Han, Ming-Yi Lee, Ji Li, Brett D. Wick.

Author/creator	Han, Yongsheng
Other author	Lee, Ming-Yi.
Other author	Li, Ji (Lecturer in Mathematics)
Other author	Wick, Brett D.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2022.
Description	ix, 102 pages ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Hardy spaces. Maximal functions. Littlewood-Paley theory. Singular integrals.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 279, Number 1373
Contents	Introduction and Statement of Main Results, Applications -- Flag Littlewood-Paley Estimate: F (f ) , F (f ) and F (U ) -- Estimates of Area Functions, Maximal Functions and Riesz Transforms via Flag Poisson Integral Technique -- Flag Maximal Functions: from Poisson Kernel to General Schwartz Kernels -- Atomic Decompositions of Flag Hardy Spaces -- Estimates of Riesz Transforms and Area Function via Atomic Decomposition.
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022048346
ISBN	9781470453459 (paperback)
ISBN	(epub)

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Maximal functions, Littlewood-Paley theory, Riesz transforms and atomic decomposition in the multi-parameter flag setting / Yongsheng Han, Ming-Yi Lee, Ji Li, Brett D. Wick.

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