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  • © 1983

Theory of Function Spaces

Birkhäuser

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

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  • ISBN: 978-3-0346-0416-1
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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
  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. Weighted Function Spaces on R n

    • Hans Triebel
    Pages 254-259
  8. Periodic Function Spaces

    • Hans Triebel
    Pages 264-268
  9. Further Types of Function Spaces

    • Hans Triebel
    Pages 269-273
  10. Back Matter

    Pages 274-285

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

 It is written in a concise but well readable style. (…) This book can be best recommended to researchers and advanced students working on functional analysis or functional analytic methods for partial differential operators or equations.

- Zentralblatt MATH

 The noteworthy new items in the book are: the use of maximal functions, treatment of BMO spaces, treatment of Beurling ultradistributions as well as addition of new results, too numerous to mention, obtained within the last 7 years or so.

- Mathematical Reviews

Keywords

  • analytic function
  • differential equation
  • differential operator
  • distribution
  • equation
  • function

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: 978-3-0346-0415-4

  • eBook ISBN: 978-3-0346-0416-1

  • Series ISSN: 2197-1803

  • Series E-ISSN: 2197-1811

  • Edition Number: 1

  • Number of Pages: IV, 281

  • Topics: Humanities and Social Sciences

Buying options

eBook
USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-0346-0416-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 84.99
Price excludes VAT (USA)