| Preface Chapter I Fourier Series 1. Fourier Series of Functions 2. Fourier Series of Continuous Functions 3. Elementary Properties of Fourier Series 4. Fourier Series of Functionals 5. Notes; Further Results and Problems Chapter II Cesaro Summability 1. (C, 1) Summability 2. Fejer's Kernel 3, Characterization of Fourier Series of Functions and Measures 4. A.E. Convergence of (C, 1) Means of Summable Functions 5. Notes; Further Results and Problems Chapter III Norm Convergence of Fourier Series 1. The Case L2(T); Hilbert Space 2. Norm Convergence in L'(T), 1 < p < 3. The Conjugate Mapping 4. More on Integrable Functions 5. Integral Representation of the Conjugate Operator 6. The Truncated Hilbert Transform 7. Notes; Further Results and Problems Chapter IV The Basic Principles 1. The Calder6n-Zygmund Interval Decomposition 2. The Hardy-Littlewood Maximal Function 3. The Calder6n-Zygmund Decomposition 4. The Marcinkiewicz Interpolation Theorem 5. Extrapolation and the Zygmund L In L Class 6. The Banach Continuity Principle and a.e. Convergence 7. Notes; Further Results and Problems Chapter V The Hilbert Transform and Multipliers 1. Existence of the Hilbert Transform of Integrable Functions 2. The Hilbert Transform in LP(T), 1 < p < 00 3. Limiting Results 4. Multipliers 5. Notes; Further Results and Problems Chapter VI Paley's Theorem and Fractional Integration 1. Paley's Theorem 2. Fractional Integration 3. Multipliers 4. Notes; Further Results and Problems Chapter VII Harmonic and Subharmonic Functions 1. Abel Summability, Nontangential Convergence 2. The Poisson and Conjugate Poisson Kernels 3. Harmonic Functions 4. Further Properties of Harmonic Functions and Subharmonic Functions 5. Harnack's and Mean Value Inequalities 6. Notes; Further Results and Problems Chapter VIII Oscillation of Functions 1. Mean Oscillation of Functions 2. The Maximal Operator and BMO 3. The Conjugate of Bounded and BMO Functions 4. Wk-Lp and Ks. Interpolation 5. Lipschitz and Morrey Spaces 6. Notes; Further Results and Problems Chapter IX Ap Weights Chapter X More about Rn Chapter XI Calderon-Zygmund Singular Integral Operators Chapter XII The Littlewood-Paley Theory Chapter XIII The Good λPrinciple Chapter XIV Hardy Spaces of Severla Real Variables Chapter XV Carleson Measures Chapter XVI Cauchy Integrals on Lipschitz Curves Chapter XVII Boundary Value Problems on C-Domains |
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