Authors:
- 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
Part of the book series: Developments in Mathematics (DEVM, volume 56)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“This voluminous book provides an exhaustive and self-contained treatment of several spaces related to Besov spaces. The useful applications of Besov spaces and Triebel-Lizorkin spaces to partial differential equations allow the reader to examine in detail many properties of the solutions of the equations.” (Maria Alessandra Ragusa, zbMATH 1414.46004, 2019)
Authors and Affiliations
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Department of Mathematics and Information Science, Tokyo Metropolitan University, Tokyo, Japan
Yoshihiro Sawano
Bibliographic Information
Book Title: Theory of Besov Spaces
Authors: Yoshihiro Sawano
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-981-13-0836-9
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-0835-2Published: 20 November 2018
eBook ISBN: 978-981-13-0836-9Published: 04 November 2018
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XXIII, 945
Number of Illustrations: 12 b/w illustrations
Topics: Fourier Analysis, Functional Analysis, Real Functions