Singular Integrals and Related Topics

Shanzhen Lu; Young Ding; Dunyan Yan9789812706232, 981-270-623-2

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.

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Table of contents :
Contents……Page 8
Preface……Page 6
1.1 Hardy-Littlewood maximal operator……Page 10
1.2 Calder on-Zygmund decomposition……Page 18
1.3 Marcinkiewicz interpolation theorem……Page 24
1.4 Weighted norm inequalities……Page 30
1.5 Notes and references……Page 44
2 Singular Integral Operators……Page 46
2.1 Calder on-Zygmund singular integral operators……Page 49
2.2 Singular integral operators with homogeneous kernels……Page 87
2.3 Singular integral operators with rough kernels……Page 101
2.4 Commutators of singular integral operators……Page 128
2.5 Notes and references……Page 140
3 Fractional Integral Operators……Page 142
3.1 Riesz potential……Page 143
3.2 Weighted boundedness of Riesz potential……Page 146
3.3 Fractional integral operator with homogeneous kernels……Page 153
3.4 Weighted boundedness of T……Page 157
3.5 Commutators of Riesz potential……Page 167
3.6 Commutators of fractional integrals with rough kernels……Page 171
3.7 Notes and references……Page 175
4.1 Oscillatory singular integrals with homogeneous smooth kernels……Page 178
4.2 Oscillatory singular integrals with rough kernels……Page 195
4.3 Oscillatory singular integrals with standard kernels……Page 206
4.4 Multilinear oscillatory singular integrals with rough kernels……Page 211
4.5 Multilinear oscillatory singular integrals with standard kernels……Page 222
4.6 Notes and references……Page 239
5 Littlewood-Paley Operator……Page 242
5.1 Littlewood-Paley g function……Page 243
5.2 Weighted Littlewood-Paley theory……Page 250
5.3 Littlewood-Paley g function with rough kernel……Page 256
5.4 Notes and references……Page 268
Bibliography……Page 270
Index……Page 280