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Theory of Function Spaces

  • Book
  • © 1983

Overview

Authors:
  1. Hans Triebel

    1. Fak. Mathematik/Informatik, Inst. Mathematik, Universität Jena, Jena, Germany

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Part of the book series: Modern Birkhäuser Classics (MBC)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Spaces of Entire Analytic Functions

    • Hans Triebel
    Pages 11-32

  3. Function Spaces on R n

    • Hans Triebel
    Pages 33-187

  4. Function Spaces on Domains

    • Hans Triebel
    Pages 188-211

  5. Regular Elliptic Differential Equations

    • Hans Triebel
    Pages 212-236

  6. Homogeneous Function Spaces

    • Hans Triebel
    Pages 237-244

  7. Ultra-Distributions and Weighted Spaces of Entire Analytic Functions

    • Hans Triebel
    Pages 245-253

  8. Weighted Function Spaces on R n

    • Hans Triebel
    Pages 254-259

  9. Weighted Function Spaces on Domains and Degenerate Elliptic Differential Equations

    • Hans Triebel
    Pages 260-263

  10. Periodic Function Spaces

    • Hans Triebel
    Pages 264-268

  11. Further Types of Function Spaces

    • Hans Triebel
    Pages 269-273

  12. Back Matter

    Pages 274-285
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Keywords

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.

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

  • Fak. Mathematik/Informatik, Inst. Mathematik, Universität Jena, Jena, Germany

    Hans Triebel

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

  • 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

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