Hardy spaces on homogeneous groups / Gerald B. Folland, Elias M. Stein.

Format:

Book

Author/Creator:

Folland, G. B., author.

Stein, Elias M., 1931-2018, author.

Series:

Mathematical Notes ; 107

Language:

English

Subjects (All):

Functions of real variables.

Hardy spaces.

Lie groups.

Physical Description:

1 online resource (302 pages) : illustrations

Place of Publication:

Princeton, New Jersey : Princeton University Press : University of Tokyo Press, [1982]

Summary:

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group.The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

Contents:

Frontmatter

TABLE OF CONTENTS

INTRODUCTION

Remarks on Notation

CHAPTER 1 Background on Homogeneous Groups

CHAPTER 2 Maximal Functions and Atoms

CHAPTER 3 Decomposition and Interpolation Theorems

CHAPTER 4 Other Maximal Function Characterizations of HP

CHAPTER 5 Duals of HP spaces: Campanato Spaces

CHAPTER 6 Convolution Operators on HP

CHAPTER 7 Characterization of HP by Square Functions: The Lusin and Littlewood-Paley Functions

CHAPTER 8 Boundary Value Problems

BIBLIOGRAPHY

Index of Terminology

Index of Notation

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9780691222455

0691222452

OCLC:

1312726252