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Preface
Chapter 1 Lp Space and Interpolation
1.1 Lp and Week Lp
1.2 Convolution and Approximate Identities
1.3 Interpolation
1.4 Lorentz Space
Chapter 2 Maximal Functions ,Fourier Transform ,and Distributions
2.1 Maximal Functions
2.2 The Schwartz Class and the Fourier Transform
2.3 The Class of Tempered Distributions
2.4 More about Distributions and the Fourier Transform
2.5 Convolution Operators on Lp Spaces and Multipliers
Chapter 3 Fourier Analysis on the Torus
3.1 Fourier Coefficients
3.2 Decay of Fourier Coefficients
3.3 Pointwise Convergence of Fourier Series
3.4 Divergence of Fourier Series and Bochner-Riesz Summablility
3.5 The Conjugate Function and Convergence in Norm
3.6 Multipliers ,Transference,and Almost Everywhere Convergence
3.7 Lacunary Series
Chapter 4 Singular Integrals of Convolution Type
4.1 The Hibert Transform and the Riesz Transforms
4.2 Homogeneous Singular Integrals and the Method of Rotations
4.3 The Calderon-zygmund Decomposition and Singular Integrals
4.4 Sufficient Conditions for Lp Boundedness
4.5 Vector-Valued Inequalities
4.6 Vector-Valued Singular Integrals
Chapter 5 Little wood-paley Theory and Multipliers
5.1 Little wood-paley Theory
5.2 Two Multiplier Therrems
5.3 Applications of Little wood-paley Theory
5.4 The Haar System,Conditional Expectation,and Martingales
5.5 The Spherical Maximal Function
5.6 Wavelets
Chapter 6 Smoothness and Function Spaces
6.1 Riesz Potentials ,Bessel Potentials ,and Fractional Integrals
6.2 Sobolev Spaces
6.3 Lipschitz Spaces
6.4 Hardy Spaces
6.5 Besov-Lipschitz and Triebel-Lizorkin Spaces
6.6 Atomic Decomposition
6.7 Singular Integrals on Function Spaces
Chapter 7 BMO and Carleson Measures
7.1 Functions of Bounded Mean Oscillation
7.2 Duality Between H1 and Carleson Measures
7.3 Nontangential Maximal Functions and Carleson Measures
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Chapter 8 Singular Integrals of Nonconvolution Type
Chapter 9 Weighted Intequalities
Chapter 10 Boundedness and Convergence of Fourier Integrals
Appendix A Gamma and Beta Functions
Appendix B Bessel Functions
Appendix C Rademacher Functions
Appendix D Spherical Coordinates
Appendix E Some Trigonometric Identities and Inequalities
Appendix F Summation by Parts
Appendix G Basic Functional Analysis
Appendix H The Minimax Lemma
Appendix I The Schur Lemma
Appendix J The Whitney Decomposition of open sets in Rn
Appendix K Smoothness and Vanishing Moments
Bibliography
Index of Notation
Index
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