Morrey and Campanato Meet Besov, Lizorkin and Triebel
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 Campa
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2005
Wen Yuan · Winfried Sickel · Dachun Yang
Morrey and Campanato Meet Besov, Lizorkin and Triebel
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Wen Yuan School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 People’s Republic of China [email protected]
Dachun Yang (Corresponding Author) School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 People’s Republic of China [email protected]
Winfried Sickel Mathematisches Institut Friedrich-Schiller-Universit¨at Jena Ernst-Abbe-Platz 2 Jena 07743 Germany [email protected]
Corresponding author, who is supported by the National Natural Science Foundation (Grant No. 10871025) of China.
ISBN: 978-3-642-14605-3 e-ISBN: 978-3-642-14606-0 DOI: 10.1007/978-3-642-14606-0 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2010935182 Mathematics Subject Classification (2010): 42B35, 46E35, 42B25, 42C40, 42B15, 47G30, 47H30 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper springer.com
Preface
This book is based on three developments in the theory of function spaces. As the first we wish to mention Besov and Triebel-Lizorkin spaces. These scales Bsp, q (Rn ) and Fp,s q(Rn ) allow a unified approach to various types of function spaces which have been known before like H¨older-Zygmund spaces, Sobolev spaces, Slobodeckij spaces and Bessel-potential spaces. Over the last 60 years these scales have proved their usefulness, there are hundreds of papers and many books using these scales in various connections. In a certain sense all these spaces are connected with the usual Lebesgue spaces L p (Rn ). The second source we wish to mention is Morrey and Campanato spaces. Since several years there is an increasing interest in function spaces built on Morrey spaces and leading to generalizations of Campanato spaces. This interest originates, at least partly, in some applications in the field of Navier-Stokes equations. Th
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