Classical Fourier Analysis

• Main Author: Grafakos, Loukas (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2014.
• Edition: 3rd ed. 2014.
• Series: Graduate Texts in Mathematics, 249
• Subjects: 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...

Table of Contents:

• 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.