By: Shanzhen Lu, Yong Ding, Dunyan Yan

Hardcover

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This book introduces some important progress in the theory of Calderon-Zygmund singular integrals, oscillatory singular integrals, and Littlewood-Paley theory over the last decade. It includes some important research results by the authors and their cooperators, such as singular integrals with rough kernels on Block spaces and Hardy spaces, the criterion on boundedness of oscillatory singular integrals, and boundedness of the rough Marcinkiewicz integrals. These results have frequently been cited in many published papers.

"All the results in the book are written in the context of Euclidean spaces and they are very clearly presented. Many of the results in the last three chapters of the book reflect several advancements in the theory made by the Beijing harmonic analysis school of Professor Shanzhen Lu. This book provides excellent background material for further research in the topics that it covers in the last three chapters."Professor Loukas GrafakosUniversity of Missouri

Preface	p. v
Hardy-Littlewood Maximal Operator	p. 1
Hardy-Littlewood maximal operator	p. 1
Calderon-Zygmund decomposition	p. 9
Marcinkiewicz interpolation theorem	p. 15
Weighted norm inequalities	p. 21
Notes and references	p. 35
Singular Integral Operators	p. 37
Calderon-Zygmund singular integral operators	p. 40
Singular integral operators with homogeneous kernels	p. 78
Singular integral operators with rough kernels	p. 92
Commutators of singular integral operators	p. 119
Notes and references	p. 131
Fractional Integral Operators	p. 133
Riesz potential	p. 134
Weighted boundedness of Riesz potential	p. 137
Fractional integral operator with homogeneous kernels	p. 144
Weighted boundedness of T[Omega],[alpha]	p. 148
Commutators of Riesz potential	p. 158
Commutators of fractional integrals with rough kernels	p. 162
Notes and references	p. 166
Oscillatory Singular Integrals	p. 169
Oscillatory singular integrals with homogeneous smooth kernels	p. 169
Oscillatory singular integrals with rough kernels	p. 186
Oscillatory singular integrals with standard kernels	p. 197
Multilinear oscillatory singular integrals with rough kernels	p. 202
Multilinear oscillatory singular integrals with standard kernels	p. 213
Notes and references	p. 230
Littlewood-Paley Operator	p. 233
Littlewood-Paley g function	p. 234
Weighted Littlewood-Paley theory	p. 241
Littlewood-Paley g function with rough kernel	p. 247
Notes and references	p. 259
Bibliography	p. 261
Index	p. 271
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789812706232
ISBN-10: 9812706232
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 280
Published: 19th April 2007
Dimensions (cm): 22.5 x 16.0  x 2.0
Weight (kg): 0.934