| |
| |
| Preface | |
| |
| |
| |
| Fourier Series | |
| |
| |
| |
| Fourier Series of Functions | |
| |
| |
| |
| Fourier Series of Continuous Functions | |
| |
| |
| |
| Elementary Properties of Fourier Series | |
| |
| |
| |
| Fourier Series of Functionals | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Cesaro Summability | |
| |
| |
| |
| (C, 1) Summability | |
| |
| |
| |
| Fejer's Kernel | |
| |
| |
| |
| Characterization of Fourier Series of Functions and Measures | |
| |
| |
| |
| A.E. Convergence of (C, 1) Means of Summable Functions | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Norm Convergence of Fourier Series | |
| |
| |
| |
| The Case L[superscript 2](T); Hilbert Space | |
| |
| |
| |
| Norm Convergence in L[superscript p] (T), 1 [less than or equal] p [less than or equal] [infinity] | |
| |
| |
| |
| The Conjugate Mapping | |
| |
| |
| |
| More on Integrable Functions | |
| |
| |
| |
| Integral Representation of the Conjugate Operator | |
| |
| |
| |
| The Truncated Hilbert Transform | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| The Basic Principles | |
| |
| |
| |
| The Calderon-Zygmund Interval Decomposition | |
| |
| |
| |
| The Hardy-Littlewood Maximal Function | |
| |
| |
| |
| The Calderon-Zygmund Decomposition | |
| |
| |
| |
| The Marcinkiewicz Interpolation Theorem | |
| |
| |
| |
| Extrapolation and the Zygmund L ln L Class | |
| |
| |
| |
| The Banach Continuity Principle and a. e. Convergence | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| The Hilbert Transform and Multipliers | |
| |
| |
| |
| Existence of the Hilbert Transform of Integrable Functions | |
| |
| |
| |
| The Hilbert Transform in L[superscript p](T), 1 [less than or equal] p [less than sign] [infinity] | |
| |
| |
| |
| Limiting Results | |
| |
| |
| |
| Multipliers | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Paley's Theorem and Fractional Integration | |
| |
| |
| |
| Paley's Theorem | |
| |
| |
| |
| Fractional Integration | |
| |
| |
| |
| Multipliers | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Harmonic and Subharmonic Functions | |
| |
| |
| |
| Abel Summability, Nontangential Convergence | |
| |
| |
| |
| The Poisson and Conjugate Poisson Kernels | |
| |
| |
| |
| Harmonic Functions | |
| |
| |
| |
| Further Properties of Harmonic Functions and Subharmonic Functions | |
| |
| |
| |
| Harnack's and Mean Value Inequalities | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Oscillation of Functions | |
| |
| |
| |
| Mean Oscillation of Functions | |
| |
| |
| |
| The Maximal Operator and BMO | |
| |
| |
| |
| The Conjugate of Bounded and BMO Functions | |
| |
| |
| |
| Wk-L[superscript p] and K[subscript f]. Interpolation | |
| |
| |
| |
| Lipschitz and Morrey Spaces | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| A[subscript p] Weights | |
| |
| |
| |
| The Hardy-Littlewood Maximal Theorem for Regular Measures | |
| |
| |
| |
| A[subscript p] Weights and the Hardy-Littlewood Maximal Function | |
| |
| |
| |
| A[subscript 1] Weights | |
| |
| |
| |
| A[subscript p] Weights, p [greater than sign] 1 | |
| |
| |
| |
| Factorization of A[subscript p] Weights | |
| |
| |
| |
| A[subscript p] and BMO | |
| |
| |
| |
| An Extrapolation Result | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| More about R[superscript n] | |
| |
| |
| |
| Distributions, Fourier Transforms | |
| |
| |
| |
| Translation Invariant Operators. Multipliers | |
| |
| |
| |
| The Hilbert and Riesz Transforms | |
| |
| |
| |
| Sobolev and Poincare Inequalities | |
| |
| |
| |
| Calderon-Zygmund Singular Integral Operators | |
| |
| |
| |
| The Benedek-Calderon-Panzone Principle | |
| |
| |
| |
| A Theorem of Zo | |
| |
| |
| |
| Convolution Operators | |
| |
| |
| |
| Cotlar's Lemma | |
| |
| |
| |
| Calderon-Zygmund Singular Integral Operators | |
| |
| |
| |
| Maximal Calderon-Zygmund Singular Integral Operators | |
| |
| |
| |
| Singular Integral Operators in L[superscript infinity] (R[superscript n]) | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| The Littlewood-Paley Theory | |
| |
| |
| |
| Vector-Valued Inequalities | |
| |
| |
| |
| Vector-Valued Singular Integral Operators | |
| |
| |
| |
| The Littlewood-Paley g Function | |
| |
| |
| |
| The Lusin Area Function and the Littlewood-Paley g*[subscript lambda] Function | |
| |
| |
| |
| Hormander's Multiplier Theorem | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| The Good [lambda] Principle | |
| |
| |
| |
| Good [lambda] Inequalities | |
| |
| |
| |
| Weighted Norm Inequalities for Maximal CZ Singular Integral Operators | |
| |
| |
| |
| Weighted Weak-Type (1,1) Estimates for CZ Singular Integral Operators | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Hardy Spaces of Several Real Variables | |
| |
| |
| |
| Atomic Decomposition | |
| |
| |
| |
| Maximal Function Characterization of Hardy Spaces | |
| |
| |
| |
| Systems of Conjugate Functions | |
| |
| |
| |
| Multipliers | |
| |
| |
| |
| Interpolation | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Carleson Measures | |
| |
| |
| |
| Carleson Measures | |
| |
| |
| |
| Duals of Hardy Spaces | |
| |
| |
| |
| Tent Spaces | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Cauchy Integrals on Lipschitz Curves | |
| |
| |
| |
| Cauchy Integrals on Lipschitz Curves | |
| |
| |
| |
| Related Operators | |
| |
| |
| |
| The T1 Theorem | |
| |
| |
| |
| Notes; Further Results and Problems | |
| |
| |
| |
| Boundary Value Problems on C[superscript 1]-Domains | |
| |
| |
| |
| The Double and Single Layer Potentials on a C[superscript 1]-Domain | |
| |
| |
| |
| The Dirichlet and Neumann Problems | |
| |
| |
| |
| Notes | |
| |
| |
| Bibliography | |
| |
| |
| Index | |