Classical Fourier analysis

書誌事項

Classical Fourier analysis

Loukas Grafakos

(Graduate texts in mathematics, 249)

Springer Science+Business Media, c2014

3rd ed

  • : softcover

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注記

"Originally publisehd by Springer, New York, Inc in 2014. Softcover reprint of the hardcover 3rd edition 2014"--T.p. verso

Includes bibliographical references (p. 617-631) and index

内容説明・目次

内容説明

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. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on "Weighted Inequalities," which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.

目次

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.

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詳細情報

  • NII書誌ID(NCID)
    BB2567030X
  • ISBN
    • 9781493939169
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    New York
  • ページ数/冊数
    xvii, 638 p.
  • 大きさ
    24 cm
  • 件名
  • 親書誌ID
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