Classical Fourier Analysis

• Κύριος συγγραφέας: Grafakos, Loukas (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2014.
• Έκδοση: 3rd ed. 2014.
• Σειρά: Graduate Texts in Mathematics, 249
• Θέματα: Mathematics.; Harmonic analysis.; Fourier analysis.; Functional analysis.; Fourier Analysis.; Abstract Harmonic Analysis.; Functional Analysis.

The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readershi...

Πίνακας περιεχομένων:

• Preface
• 1. Lp Spaces and Interpolation
• 2. Maximal Functions, Fourier Transform, and Distributions
• 3. Fourier Series
• 4. Topics on Fourier Series
• 5. Singular Integrals of Convolution Type
• 6. Littlewood–Paley Theory and Multipliers
• 7. Weighted Inequalities
• A. Gamma and Beta Functions
• B. Bessel Functions
• C. Rademacher Functions
• D. Spherical Coordinates
• E. Some Trigonometric Identities and Inequalities
• F. Summation by Parts
• G. Basic Functional Analysis
• H. The Minimax Lemma
• I. Taylor's and Mean Value Theorem in Several Variables
• J. The Whitney Decomposition of Open Sets in Rn
• Glossary
• References
• Index.