奇异积分和相关论题 英文 影印版PDF电子书下载

1 HARDY-LITTLEWOOD MAXIMAL OPERATOR 1

1.1 Hardy-Littlewood maximal operator 1

1.2 Calderón-Zygmund decomposition 9

1.3 Marcinkiewicz interpolation theorem 15

1.4 Weighted norm inequalities 21

1.5 Notes and references 35

2 SINGULAR INTEGRAL OPERATORS 37

2.1 Calderón-Zygmund singular integral operators 40

2.2 Singular integral operators with homogeneous kernels 78

2.3 Singular integral operators with rough kernels 92

2.4 Commutators of singular integral operators 119

2.5 Notes and references 131

3 FRACTIONAL INTEGRAL OPERATORS 133

3.1 Riesz potential 134

3.2 Weighted boundedness of Riesz potential 137

3.3 Fractional integral operator with homogeneous kernels 144

3.4 Weighted boundedness ofTΩ,α 148

3.5 Commutators of Riesz potential 158

3.6 Commutators of fraction integrals with rough kernels 162

3.7 Notes and references 166

4 OSCILLATORY SINGULAR INTEGRALS 169

4.1 Oscillatory singular integrals with homogeneous smooth kernels 169

4.2 Oscillatory singular integrals with rough kernels 186

4.3 Oscillatory singular integrals with standard kernels 197

4.4 Multilinear oscillatory singular integrals with rough kernels 202

4.5 Multilinear oscillatory singular integrals with standard kernels 213

4.6 Notes and references 230

5 LITTLEWOOD-PALEY OPERATOR 233

5.1 Littlewood-Paley g function 234

5.2 Weighted Littlewood-Paley theory 241

5.3 Littlewood-Paley g function with rough kernel 247

5.4 Notes and references 259

Bibliography 261

Index 271