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.

Format:

Book

Author/Creator:

Han, Yongsheng, author.

Lee, Ming-Yi, author.

Li, Ji (Lecturer in Mathematics), author.

Wick, Brett D., author.

Series:

Memoirs of the American Mathematical Society ; no. 1373.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1373

Language:

English

Subjects (All):

Hardy spaces.

Maximal functions.

Littlewood-Paley theory.

Singular integrals.

Flag manifolds.

Fourier transformations.

Functions of complex variables.

Functions of several real variables.

Riesz spaces.

Physical Description:

ix, 102 pages ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, 2022.

Summary:

"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.

Contents:

Introduction and Statement of Main Results, Applications

Flag Littlewood-Paley Estimate: ||gF (f )||1, ||SF (f )||1 and ||SF (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.

Notes:

Includes bibliographical references.

ISBN:

9781470453459

1470453452

OCLC:

1343642858