Real-variable methods in harmonic analysis

Front Cover......Page 1
Title Page......Page 4
Copyright Information......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 12
1. Fourier Series of Functions......Page 14
2. Fourier Series of Continuous Functions......Page 21
3. Elementary Properties of Fourier Series......Page 26
4. Fourier Series of Functionals......Page 29
5. Notes; Further Results and Problems......Page 35
1. (C,1) Summability......Page 41
2. Fejer\'s Kernel......Page 42
3. Characterization of Fourier Series of Functions and Measures......Page 47
4. A.E. Convergence of (C,1) Means of Summable Functions......Page 54
5. Notes; Further Results and Problems......Page 56
1. The Case L²(T); Hilbert Space......Page 61
2. Norm Convergence in L^{p}(T), 1≤ p ≤∞......Page 64
3. The Conjugate Mapping......Page 65
4. More on Integrable Functions......Page 67
5. Integral Representation of the Conjugate Operator......Page 72
6. The Truncated Hilbert Transform......Page 78
7. Notes; Further Results and Problems......Page 81
1. The Calderon-Zygmund Interval Decomposition......Page 87
2. The Hardy-Littlewood Maximal Function......Page 89
3. The Calderon-Zygmund Decomposition......Page 97
4. The Marcinkiewicz Interpolation Theorem......Page 99
5. Extrapolation and the Zygmund L In L Class......Page 104
6. The Banach Continuity Principle and a.e. Convergence......Page 107
7. Notes; Further Results and Problems......Page 113
1. Existence of the Hilbert Transform of Integrable Functions......Page 123
2. The Hilbert Transform in L^{p}(T), 1≤ p <∞......Page 128
3. Limiting Results......Page 134
4. Multipliers......Page 139
5. Notes; Further Results and Problems......Page 145
1. Paley\'s Theorem......Page 155
2. Fractional Integration......Page 163
3. Multipliers......Page 169
4. Notes; Further Results and Problems......Page 171
1. Abel Summability, Nontangential Convergence......Page 180
2. The Poisson and Conjugate Poisson Kernels......Page 184
3. Harmonic Functions......Page 189
4. Further Properties of Harmonic Functions and Subharmonic Functions......Page 194
5. Harnack\'s and Mean Value Inequalities......Page 200
6. Notes; Further Results and Problems......Page 204
1. Mean Oscillation of Functions......Page 212
2. The Maximal Operator and BMO......Page 217
3. The Conjugate of Bounded and BMO Functions......Page 219
4. Wk-L^p and K_{f}. Interpolation......Page 222
5. Lipschitz and Morrey Spaces......Page 226
6. Notes; Further Results and Problems......Page 229
1. The Hardy-Littlewood Maximal Theorem for Regular Measures......Page 236
2. A_p Weights and the Hardy-Littlewood Maximal Function......Page 238
3. A_1 Weights......Page 241
4. A_p Weights, p > 1......Page 246
5. Factorization of A_p Weights......Page 250
6. A_p and BMO......Page 253
7. An Extrapolation Result......Page 255
8. Notes; Further Results and Problems......Page 260
1. Distributions. Fourier Transforms......Page 272
2. Translation Invariant Operators. Multipliers......Page 276
3. The Hilbert and Riesz Transforms......Page 279
4. Sobolev and Poincare Inequalities......Page 283
1. The Benedek-Calderon-Panzone Principle......Page 293
2. A Theorem of Zo......Page 295
3. Convolution Operators......Page 297
4. Cotlar\'s Lemma......Page 298
5. Calderon-Zygmund Singular Integral Operators......Page 299
6. Maximal Calderon-Zygmund Singular Integral Operators......Page 304
7. Singular Integral Operators in L^{∞}(Rⁿ)......Page 307
8. Notes; Further Results and Problems......Page 308
1. Vector-Valued Inequalities......Page 316
2. Vector-Valued Singular Integral Operators......Page 320
3. The Littlewood-Paley g Function......Page 322
4. The Lusin Area Function and the Littlewood-Paley g_{λ}^{*} Function......Page 327
5. Hormander\'s Multiplier Theorem......Page 331
6. Notes; Further Results and Problems......Page 334
1. Good λ Inequalities......Page 341
2. Weighted Norm Inequalities for Maximal CZ Singular Integral Operators......Page 343
3. Weighted Weak-Type (1,1) Estimates for CZ Singular Integral Operators......Page 347
4. Notes; Further Results and Problems......Page 350
1. Atomic Decomposition......Page 353
2. Maximal Function Characterization of Hardy Spaces......Page 363
3. Systems of Conjugate Functions......Page 369
4. Multipliers......Page 372
5. Interpolation......Page 376
6. Notes; Further Results and Problems......Page 379
1. Carleson Measures......Page 385
2. Duals of Hardy Spaces......Page 387
3. Tent Spaces......Page 391
4. Notes; Further Results and Problems......Page 396
1. Cauchy Integrals on Lipschitz Curves......Page 405
2. Related Operators......Page 421
3. The T1 Theorem......Page 425
4. Notes; Further Results and Problems......Page 429
1. The Double and Single Layer Potentials on a C¹-Domain......Page 437
2. The Dirichlet and Neumann Problems......Page 451
3. Notes......Page 457
Bibliography......Page 459
Index......Page 470