Real-Variable Methods in Harmonic Analysis
, by Torchinsky, Alberto
- ISBN: 9780126954616 | 0126954615
- Cover: Paperback
- Copyright: 10/1/1986
| 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 |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
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