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Preface | p. xi |
Fourier Series | |
Fourier Series of Functions | p. 1 |
Fourier Series of Continuous Functions | p. 8 |
Elementary Properties of Fourier Series | p. 13 |
Fourier Series of Functionals | p. 16 |
Notes; Further Results and Problems | p. 22 |
Cesaro Summability | |
(C, 1) Summability | p. 28 |
Fejer's Kernel | p. 29 |
Characterization of Fourier Series of Functions and Measures | p. 34 |
A.E. Convergence of (C, 1) Means of Summable Functions | p. 41 |
Notes; Further Results and Problems | p. 43 |
Norm Convergence of Fourier Series | |
The Case L[superscript 2](T); Hilbert Space | p. 48 |
Norm Convergence in L[superscript p] (T), 1 [less than or equal] p [less than or equal] [infinity] | p. 51 |
The Conjugate Mapping | p. 52 |
More on Integrable Functions | p. 54 |
Integral Representation of the Conjugate Operator | p. 59 |
The Truncated Hilbert Transform | p. 65 |
Notes; Further Results and Problems | p. 68 |
The Basic Principles | |
The Calderon-Zygmund Interval Decomposition | p. 74 |
The Hardy-Littlewood Maximal Function | p. 76 |
The Calderon-Zygmund Decomposition | p. 84 |
The Marcinkiewicz Interpolation Theorem | p. 86 |
Extrapolation and the Zygmund L ln L Class | p. 91 |
The Banach Continuity Principle and a. e. Convergence | p. 94 |
Notes; Further Results and Problems | p. 100 |
The Hilbert Transform and Multipliers | |
Existence of the Hilbert Transform of Integrable Functions | p. 110 |
The Hilbert Transform in L[superscript p](T), 1 [less than or equal] p [less than sign] [infinity] | p. 115 |
Limiting Results | p. 121 |
Multipliers | p. 126 |
Notes; Further Results and Problems | p. 132 |
Paley's Theorem and Fractional Integration | |
Paley's Theorem | p. 142 |
Fractional Integration | p. 150 |
Multipliers | p. 156 |
Notes; Further Results and Problems | p. 158 |
Harmonic and Subharmonic Functions | |
Abel Summability, Nontangential Convergence | p. 167 |
The Poisson and Conjugate Poisson Kernels | p. 171 |
Harmonic Functions | p. 176 |
Further Properties of Harmonic Functions and Subharmonic Functions | p. 181 |
Harnack's and Mean Value Inequalities | p. 187 |
Notes; Further Results and Problems | p. 191 |
Oscillation of Functions | |
Mean Oscillation of Functions | p. 199 |
The Maximal Operator and BMO | p. 204 |
The Conjugate of Bounded and BMO Functions | p. 206 |
Wk-L[superscript p] and K[subscript f]. Interpolation | p. 209 |
Lipschitz and Morrey Spaces | p. 213 |
Notes; Further Results and Problems | p. 216 |
A[subscript p] Weights | |
The Hardy-Littlewood Maximal Theorem for Regular Measures | p. 223 |
A[subscript p] Weights and the Hardy-Littlewood Maximal Function | p. 225 |
A[subscript 1] Weights | p. 228 |
A[subscript p] Weights, p [greater than sign] 1 | p. 233 |
Factorization of A[subscript p] Weights | p. 237 |
A[subscript p] and BMO | p. 240 |
An Extrapolation Result | p. 242 |
Notes; Further Results and Problems | p. 247 |
More about R[superscript n] | |
Distributions, Fourier Transforms | p. 259 |
Translation Invariant Operators. Multipliers | p. 263 |
The Hilbert and Riesz Transforms | p. 266 |
Sobolev and Poincare Inequalities | p. 270 |
Calderon-Zygmund Singular Integral Operators | |
The Benedek-Calderon-Panzone Principle | p. 280 |
A Theorem of Zo | p. 282 |
Convolution Operators | p. 284 |
Cotlar's Lemma | p. 285 |
Calderon-Zygmund Singular Integral Operators | p. 286 |
Maximal Calderon-Zygmund Singular Integral Operators | p. 291 |
Singular Integral Operators in L[superscript infinity] (R[superscript n]) | p. 294 |
Notes; Further Results and Problems | p. 295 |
The Littlewood-Paley Theory | |
Vector-Valued Inequalities | p. 303 |
Vector-Valued Singular Integral Operators | p. 307 |
The Littlewood-Paley g Function | p. 309 |
The Lusin Area Function and the Littlewood-Paley g*[subscript lambda] Function | p. 314 |
Hormander's Multiplier Theorem | p. 318 |
Notes; Further Results and Problems | p. 321 |
The Good [lambda] Principle | |
Good [lambda] Inequalities | p. 328 |
Weighted Norm Inequalities for Maximal CZ Singular Integral Operators | p. 330 |
Weighted Weak-Type (1,1) Estimates for CZ Singular Integral Operators | p. 334 |
Notes; Further Results and Problems | p. 337 |
Hardy Spaces of Several Real Variables | |
Atomic Decomposition | p. 340 |
Maximal Function Characterization of Hardy Spaces | p. 350 |
Systems of Conjugate Functions | p. 356 |
Multipliers | p. 359 |
Interpolation | p. 363 |
Notes; Further Results and Problems | p. 366 |
Carleson Measures | |
Carleson Measures | p. 372 |
Duals of Hardy Spaces | p. 374 |
Tent Spaces | p. 378 |
Notes; Further Results and Problems | p. 383 |
Cauchy Integrals on Lipschitz Curves | |
Cauchy Integrals on Lipschitz Curves | p. 392 |
Related Operators | p. 408 |
The T1 Theorem | p. 412 |
Notes; Further Results and Problems | p. 416 |
Boundary Value Problems on C[superscript 1]-Domains | |
The Double and Single Layer Potentials on a C[superscript 1]-Domain | p. 424 |
The Dirichlet and Neumann Problems | p. 438 |
Notes | p. 444 |
Bibliography | p. 446 |
Index | p. 457 |
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