Multi-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals / Guozhen Lu, Jiawei Shen, and Lu Zhang.

Format:

Book

Author/Creator:

Lu, Guozhen, author.

Shen, Jiawei (Researcher in mathematics), author.

Zhang, Lu (Researcher in mathematics), author.

Series:

Memoirs of the American Mathematical Society ; Volume 281.

Memoirs of the American Mathematical Society Series ; Volume 281

Language:

English

Subjects (All):

Hardy spaces.

Singular integrals.

Littlewood-Paley theory.

Physical Description:

1 online resource (100 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"The main purpose of this paper is to establish the theory of the multi-parameter Hardy spaces Hp (0 [less than] p [less than or equal to] 1) associated to a class of multi-parameter singular integrals extensively studied in the recent book of B. Street (2014), where the Lp (1 [less than] p [less than] [infinity]) estimates are proved for this class of singular integrals. This class of multi-parameter singular integrals are intrinsic to the underlying multi-parameter Carnot-Caratheodory geometry, where the quantitative Frobenius theorem was established by B. Street (2011), and are closely related to both the one-parameter and multi-parameter settings of singular Radon transforms considered by Stein and Street (2011, 2012a, 2012b, 2013). More precisely, Street (2014) studied the Lp (1 [less than] p [less than] [infinity]) boundedness, using elementary operators, of a type of generalized multi-parameter Calderon Zygmund operators on smooth and compact manifolds, which include a certain type of singular Radon transforms. In this work, we are interested in the endpoint estimates for the singular integral operators in both one and multi-parameter settings considered by Street (2014). Actually, using the discrete Littlewood-Paley-Stein analysis, we will introduce the Hardy space Hp (0 [less than] p [less than or equal to] 1) associated with the multi-parameter structures arising from the multi-parameter Carnot-Caratheodory metrics using the appropriate discrete Littlewood-Paley-Stein square functions, and then establish the Hardy space boundedness of singular integrals in both the single and multi-parameter settings. Our approach is much inspired by the work of Street (2014) where he introduced the notions of elementary operators so that the type of singular integrals under consideration can be decomposed into elementary operators"-- Provided by publisher.

Contents:

Cover

Title page

Chapter 1. Introduction

Acknowledgments

Chapter 2. Single-parameter theory

2.1. Singular integral operators and elementary operators

2.2. Discrete Littlewood-Paley-Stein theory and Hardy spaces

2.3. Endpoint estimate for one-parameter singular integrals

Chapter 3. Multi-parameter setting: Product theory

3.1. Product singular integral operators

3.2. Hardy spaces on the product space

3.3. Endpoint estimates on product singular integrals

Chapter 4. General multi-parameter singular integrals and Hardy spaces

4.1. Assumptions for vector fields

4.2. Multi-parameter Hardy spaces

4.3. ^{ } boundedness of multi-parameter singular integrals

Bibliography

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references.

Other Format:

Print version: Lu, Guozhen Multi-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals

ISBN:

9781470473211

1470473216