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

Format:

Book

Author/Creator:

Han, Yongsheng.

Contributor:

Lee, Ming-Yi.

Li, Ji.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.279

Language:

English

Subjects (All):

Hardy spaces.

Maximal functions.

Littlewood-Paley theory.

Singular integrals.

Physical Description:

1 online resource (118 pages)

Edition:

1st ed.

Place of Publication:

Providence : 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:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Han, Yongsheng Maximal Functions, Littlewood-Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting

ISBN:

9781470472276

1470472279

OCLC:

1343250653