Hardy spaces on homogeneous groups 069108310X, 9780691083100
The object of this monograph Is to give an exposition of the real-variable theory of Hardy spaces (H^p spaces). This the
368 11 1MB
English Pages 299 Year 1982
Table of contents :
Cover......Page 1
Series......Page 2
TABLE OF CONTENTS......Page 3
INTRODUCTION......Page 5
Remarks on Notation......Page 14
CHAPTER 1: Background on Homogeneous Groups......Page 15
A. Homogeneous Groups......Page 16
B. Convolutions......Page 29
C. Derivatives and Polynomials......Page 34
D. The Schwartz Class......Page 49
E. Integral Representations of the $\\delta$ Function......Page 59
F. Covering Lemmas......Page 67
G. The Heat Kernel on Stratified Groups......Page 69
Notes and References......Page 75
CHAPTER 2: Maximal Functions and Atoms......Page 76
Notes and References......Page 93
CHAPTER 3: Decomposition and Interpolation Theorems......Page 94
A. The Calderon-Zygmund Decomposition......Page 95
B. The Atomic Decomposition......Page 111
C. Interpolation Theorems......Page 121
Notes and References......Page 125
A. Relationships Among Maximal Functions......Page 127
B. Construction of Commutative Approximate Identities......Page 142
Notes and References......Page 153
A. The Dual of $H^p$......Page 155
B. BM0......Page 160
C. Lipschitz Classes......Page 170
Notes and References......Page 196
A. Kernels of Type $(\\alpha,r)$......Page 198
B. A Multiplier Theorem......Page 222
Notes and References......Page 229
CHAPTER 7: Characterization of $H^p$ by Square Functions: The Lusin and Littlewood-Paley Functions......Page 231
Notes and References......Page 260
CHAPTER 8: Boundary Value Problems......Page 261
A. Temperatures on Stratified Groups......Page 262
B. Poisson Integrals on Stratified Groups......Page 267
C. Poisson Integrals on Symmetric Spaces......Page 275
Notes and References......Page 286
BIBLIOGRAPHY......Page 287
Index of Terminology......Page 295
Index of Notation......Page 297
Date-line......Page 299
Cover......Page 1
Series......Page 2
TABLE OF CONTENTS......Page 3
INTRODUCTION......Page 5
Remarks on Notation......Page 14
CHAPTER 1: Background on Homogeneous Groups......Page 15
A. Homogeneous Groups......Page 16
B. Convolutions......Page 29
C. Derivatives and Polynomials......Page 34
D. The Schwartz Class......Page 49
E. Integral Representations of the $\\delta$ Function......Page 59
F. Covering Lemmas......Page 67
G. The Heat Kernel on Stratified Groups......Page 69
Notes and References......Page 75
CHAPTER 2: Maximal Functions and Atoms......Page 76
Notes and References......Page 93
CHAPTER 3: Decomposition and Interpolation Theorems......Page 94
A. The Calderon-Zygmund Decomposition......Page 95
B. The Atomic Decomposition......Page 111
C. Interpolation Theorems......Page 121
Notes and References......Page 125
A. Relationships Among Maximal Functions......Page 127
B. Construction of Commutative Approximate Identities......Page 142
Notes and References......Page 153
A. The Dual of $H^p$......Page 155
B. BM0......Page 160
C. Lipschitz Classes......Page 170
Notes and References......Page 196
A. Kernels of Type $(\\alpha,r)$......Page 198
B. A Multiplier Theorem......Page 222
Notes and References......Page 229
CHAPTER 7: Characterization of $H^p$ by Square Functions: The Lusin and Littlewood-Paley Functions......Page 231
Notes and References......Page 260
CHAPTER 8: Boundary Value Problems......Page 261
A. Temperatures on Stratified Groups......Page 262
B. Poisson Integrals on Stratified Groups......Page 267
C. Poisson Integrals on Symmetric Spaces......Page 275
Notes and References......Page 286
BIBLIOGRAPHY......Page 287
Index of Terminology......Page 295
Index of Notation......Page 297
Date-line......Page 299
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