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© 2010

Morrey and Campanato Meet Besov, Lizorkin and Triebel

Benefits

  • 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

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2005)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 1-19
  3. Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 49-64
  4. Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 65-135
  5. Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 137-146
  6. Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 147-175
  7. Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 177-250
  8. Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 251-269
  9. Back Matter
    Pages 271-288

About this book

Introduction

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 = ∞.

Keywords

Besov-Triebel-Lizorkin spaces Calderón reproducing formula Morrey-Campanato spaces Q spaces Wavelets, atoms and molecules boundary element method character development differential operator form framework function function space theorem wavelet

Authors and affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina, People's Republic
  2. 2.Institute of MathematicsFriedrich-Schiller-University of JenaJenaGermany
  3. 3.School of Mathematical SciencesBeijing Normal UniversityBeijingChina, People's Republic

Bibliographic information

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)