Theory of Function Spaces
著者
書誌事項
Theory of Function Spaces
（Modern Birkhäuser classics）
Birkhäuser, 2010
- [1]
- 2
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注記
Bibliography: [1], p. [274]-284; 2, p. [347]-366
Includes index
"Reprint of the 1983 edition"--T.p. of [1]
[Originally published] "for sales in non-socialist countries in 1983 as volume 78 in the Monographs in Mathematics series"--T.p. verso of [1]
"Reprint of the 1992 edition"--T.p. of 2
"Originally printed under the same title as volume 84 in the Monographs in Mathematics series"--T.p. verso of 2
内容説明・目次
- 巻冊次
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[1] ISBN 9783034604154
内容説明
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where - n in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart of the book. Chapter 3 deals with corresponding spaces on smooth bounded domains in Rn. These results are applied in Chapter 4 in order to study general boundary value problems for regular elliptic differential operators in the above spaces. Shorter Chapters (1 and 5-10) are concerned with: Entire analytic functions, ultra-distributions, weighted spaces, periodic spaces, degenerate elliptic differential equations.
目次
Spaces of Entire Analytic Functions.- Function Spaces on Rn.- Function Spaces on Domains.- Regular Elliptic Differential Equations.- Homogeneous Function Spaces.- Ultra-Distributions and Weighted Spaces of Entire Analytic Functions.- Weighted Function Spaces on Rn.- Weighted Function Spaces on Domains and Degenerate Elliptic Differential Equations.- Periodic Function Spaces.- Further Types of Function Spaces.
- 巻冊次
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2 ISBN 9783034604185
内容説明
s s T h is b o ok de als w ith the the o ry of func tion s p ac e s of t y p e B and F as it s t ands pq pq at the end of the eigh ties. These t w o scales of spaces co v er man y w ell- kno w n s paces of functions a nd distributions suc h as H.. olde r-Zy gm und s pac e s , Sob ole v s pac e s , fra- tional Sob o lev s paces (prev ious ly a ls o o ft en referred to a s Bes s e l-p o ten tial s paces ), Be s o v s pac e s , i nhom oge ne ous Hardy s p ac e s , s pac e s of BM O-t y p e and l o c al appro - imation s paces whic h are clos ely c onnected with Morrey-Campanato s paces.
目次
How To Measure Smoothness.- The Spaces and :Definit.- Atoms, Oscillations, and Distinguished Representations.- Key Theorems.- Spaces on Domains.- Mapping Properties of Pseudodifferential Operators.- Spaces on Riemannian Manifolds and Lie Groups.
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