Theory of Function Spaces

  • Hans Triebel

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-x
  2. Hans Triebel
    Pages 11-32
  3. Hans Triebel
    Pages 33-187
  4. Hans Triebel
    Pages 188-211
  5. Hans Triebel
    Pages 212-236
  6. Hans Triebel
    Pages 237-244
  7. Hans Triebel
    Pages 254-259
  8. Hans Triebel
    Pages 264-268
  9. 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


analytic function differential equation differential operator distribution equation function

Authors and affiliations

  • Hans Triebel
    • 1
  1. 1.Fak. Mathematik/Informatik, Inst. MathematikUniversität JenaJenaGermany

Bibliographic information

  • DOI
  • Copyright Information Akademische Verlagsgesellschaft Geest & Porting, K.-G., Leipzig / Birkhäuser Verlag 1983
  • Publisher Name Springer, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0346-0415-4
  • Online ISBN 978-3-0346-0416-1
  • Buy this book on publisher's site