Fourier analysis / Javier Duoandikoetxea ; translated and revised by David Cruz-Uribe.

Duoandikoetxea Zuazo, Javier.
Standardized Title:
Análisis de Fourier. English
Providence, Rhode Island : American Mathematical Society, [2001]
Graduate studies in mathematics ; v. 29.
Graduate studies in mathematics ; volume 29
1 online resource (232 p.)
Fourier analysis.
Electronic books.
""Cover""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Preliminaries""; ""Chapter 1. Fourier Series and Integrals""; ""Â1. Fourier coefficients and series""; ""Â2. Criteria for pointwise convergence""; ""Â3. Fourier series of continuous functions""; ""Â4. Convergence in norm""; ""Â5. Summability methods""; ""Â6. The Fourier transform of L[sup(1)] functions""; ""Â7. The Schwartz class and tempered distributions""; ""Â8. The Fourier transform on L[sup(p)], 1 < p â?? 2""; ""Â9. The convergence and summability of Fourier integrals""; ""Â10. Notes and further results""
""Chapter 2. The Hardy-Littlewood Maximal Function""""Â1. Approximations of the identity""; ""Â2. Weak-type inequalities and almost everywhere convergence""; ""Â3. The Marcinkiewicz interpolation theorem""; ""Â4. The Hardy-Littlewood maximal function""; ""Â5. The dyadic maximal function""; ""Â6. The weak (1,1) inequality for the maximal function""; ""Â7. A weighted norm inequality""; ""Â8. Notes and further results""; ""Chapter 3. The Hilbert Transform""; ""Â1. The conjugate Poisson kernel""; ""Â2. The principal value of 1/x""; ""Â3. The theorems of M. Riesz and Kolmogorov""
""Â4. Truncated integrals and pointwise convergence""""Â5. Multipliers""; ""Â6. Notes and further results""; ""Chapter 4. Singular Integrals (I)""; ""Â1. Definition and examples""; ""Â2. The Fourier transform of the kernel""; ""Â3. The method of rotations""; ""Â4. Singular integrals with even kernel""; ""Â5. An operator algebra""; ""Â6. Singular integrals with variable kernel""; ""Â7. Notes and further results""; ""Chapter 5. Singular Integrals (II)""; ""Â1. The Calderón-Zygmund theorem""; ""Â2. Truncated integrals and the principal value""
""Â3. Generalized Calderón-Zygmund operators""""Â4. Calderón-Zygmund singular integrals""; ""Â5. A vector-valued extension""; ""Â6. Notes and further results""; ""Chapter 6. H[sup(1)] and BMO""; ""Â1. The space atomic H[sup(1)]""; ""Â2. The space BMO""; ""Â3. An interpolation result""; ""Â4. The John-Nirenberg inequality""; ""Â5. Notes and further results""; ""Chapter 7. Weighted Inequalities""; ""Â1. The A[sub(p)] condition""; ""Â2. Strong-type inequalities with weights""; ""Â3. A[sup(1)] weights and an extrapolation theorem""
""Â3. Statement and applications of the T1 theorem""
Description based upon print version of record.
Includes bibliographical references (pages 217-218) and index.
Description based on print version record.
Cruz-Uribe, David V., translator, editor.
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