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Variable Lebesgue Spaces : Foundations and Harmonic Analysis / by David V. Cruz-Uribe, Alberto Fiorenza
(Applied and Numerical Harmonic Analysis. ISSN:22965017)
版 | 1st ed. 2013. |
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出版者 | (Basel : Springer Basel : Imprint: Birkhäuser) |
出版年 | 2013 |
本文言語 | 英語 |
大きさ | IX, 312 p : online resource |
著者標目 | *Cruz-Uribe, David V author Fiorenza, Alberto author SpringerLink (Online service) |
件 名 | LCSH:Harmonic analysis LCSH:Functional analysis LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Abstract Harmonic Analysis FREE:Functional Analysis FREE:Global Analysis and Analysis on Manifolds |
一般注記 | 1 Introduction -- 2 Structure of Variable Lebesgue Spaces -- 3 The Hardy-Littlewood Maximal Operator.- 4 Beyond Log-Hölder Continuity -- 5 Extrapolation in the Variable Lebesgue Spaces -- 6 Basic Properties of Variable Sobolev Spaces -- Appendix: Open Problems -- Bibliography -- Symbol Index -- Author Index -- Subject Index. This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces HTTP:URL=https://doi.org/10.1007/978-3-0348-0548-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783034805483 |
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EB00239386 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA403-403.3 DC23:515.785 |
書誌ID | 4000117624 |
ISBN | 9783034805483 |
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※2017年9月4日以降