Details

Autor(en) / Beteiligte

• Torchinsky, Alberto

Titel

Real-variable methods in harmonic analysis

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliography and index.
• Front Cover; Real-Variable Methods in Harmonic Analysis; Copyright Page; Contents; 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. Cesàro Summability; 1. (C, 1) Summability; 2. Fejbér'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 Series1. The Case L2( T); Hilbert Space; 2. Norm Convergence in Lp(T), 1 < p< 00; 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 Calderón-Zygmund Interval Decomposition; 2. The Hardy-Littlewood Maximal Function; 3. The Calderón-Zygmund Decomposition; 4. The Marcinkiewicz Interpolation Theorem; 5 . Extrapolation and the Zygmund L In L Class
• 6. The Banach Continuity Principle and a.e. Convergence7. 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 Kernels3. 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 Kf. Interpolation; 5 . Lipschitz and Morrey Spaces; 6. Notes; Further Results and Problems; Chapter IX. Ap Weights; 1. The Hardy-Littlewood Maximal Theorem for Regular Measures
• 2. Ap Weights and the Hardy-Littlewood Maximal Function3. A1 Weights; 4. Ap Weights, p > 1; 5. Factorization of Ap Weights; 6. Ap and BMO; 7. An Extrapolation Result; 8. Notes; Further Results and Problems; Chapter X. More about Rn; 1. Distributions. Fourier Transforms; 2. Translation Invariant Operators. Multipliers; 3. The Hilbert and Riesz Transforms; 4. Sobolev and Poincaré Inequalities; Chapter XI. Calderón-Zygmund Singular Integral Operators; 1. The Bendek-Calderón-Panzone Principle; 2 . A Theorem of Zó; 3. Convolution Operators; 4. Cotlar's Lemma
• 5. Calderón-Zygmund Singular Integral Operators
• Real-variable methods in harmonic analysis
• English