Developments in Mathematics

Theory of Besov Spaces

Authors: Sawano, Yoshihiro

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  • Comprises a self-contained description of all contents, accessible to readers familiar with integration theory
  • Provides the shortest available introduction to the theory of Besov spaces, beginning with Chapter 1
  • Covers and summarizes two volumes by Hans Triebel, Theory of Function Spaces I, II
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  • ISBN 978-981-13-0836-9
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Hardcover $139.99
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About this Textbook

This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem.  Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

About the authors

Yoshihiro Sawano is a professor in Tokyo Metropolitan University.

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Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-981-13-0836-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-981-13-0835-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Theory of Besov Spaces
Authors
Series Title
Developments in Mathematics
Series Volume
56
Copyright
2018
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-0836-9
DOI
10.1007/978-981-13-0836-9
Hardcover ISBN
978-981-13-0835-2
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XXIII, 945
Number of Illustrations
12 b/w illustrations
Topics