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Classical Fourier analysis / Loukas Grafakos.

By: Material type: TextTextSeries: Graduate texts in mathematics ; 249.Publication details: New York : Springer, 2014.Edition: 3rd edDescription: xvii, 638 p. ; illustrationsISBN:
  • 9781493911936
Subject(s): DDC classification:
  • 515.2433 23 G736
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.
Summary: 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 readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.2433 G736 (Browse shelf(Opens below)) Available 135845
Total holds: 0

Includes bibliographical references and index.

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.

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 readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study.

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