Overview
- A new general framework unifying Besov-Triebel-Lizorkin spaces, Morrey spaces, Campanato spaces and Q spaces is established
- In the key theorems characterizations by atoms, molecules, wavelets, differences and oscillations are given
- Special cases of these new scales (namely Besov-Triebel-Lizorkin spaces built on Morrey spaces) have been shown to be useful in the study of Navier-Stokes equations
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2005)
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About this book
During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.
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Keywords
Table of contents (8 chapters)
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Front Matter
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Back Matter
Reviews
From the reviews:
“Besov spaces and Triebel-Lizorkin spaces are frequently used in various kinds of problems in analysis. The aim of this book is to provide a framework which includes all such spaces. … the book is well presented, with an impressive level of generality and a well-conducted quest for exhaustivity, though it also refers to some other papers. Also, not only the function spaces treated in the book but also other related function spaces promise progress in the near future, thanks to this book.” (Yoshihiro Sawano, Mathematical Reviews, Issue 2011 j)
“The present book develops the theory of the spaces … incorporating nearby other spaces such as BMO and some applications to pseudodifferential operators. This book may serve as a starting point for further research in this direction.” (Hans Triebel, Zentralblatt MATH, Vol. 1207, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Morrey and Campanato Meet Besov, Lizorkin and Triebel
Authors: Wen Yuan, Winfried Sickel, Dachun Yang
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-14606-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Softcover ISBN: 978-3-642-14605-3Published: 18 September 2010
eBook ISBN: 978-3-642-14606-0Published: 02 September 2010
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 288
Topics: Fourier Analysis, Functional Analysis, Operator Theory