Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
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About this book
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where ‑∞<s<∞ and 0<p,q≤∞, which include many classical and modern spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rn 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.
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Keywords
Table of contents (10 chapters)
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Front Matter
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Back Matter
Reviews
From the reviews:
“There is good reason to think of this book as Volume 1 in a series of (by now) celebrated books on the theory of function spaces treated in a systematic way. It turned out that for many beginners in this part of harmonic analysis this book is still the natural choice to start with. … this book can still be recommended for people who start their work in function spaces of rather general type and who have some working knowledge in functional analysis … .” (Dorothee Haroske, Zentralblatt MATH, Vol. 1235, 2012)
Authors and Affiliations
Bibliographic Information
Book Title: Theory of Function Spaces
Authors: Hans Triebel
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-0346-0416-1
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: BirkhäuserVerlag, Basel 1983
Softcover ISBN: 978-3-0346-0415-4Published: 20 August 2010
eBook ISBN: 978-3-0346-0416-1Published: 16 June 2010
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: IV, 281
Topics: Science, Humanities and Social Sciences, multidisciplinary