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Morrey and Campanato Meet Besov, Lizorkin and Triebel

  • Book
  • © 2010

Overview

Authors:
  1. Wen Yuan

    1. School of Mathematical Sciences, Beijing Normal University, Beijing, China, People's Republic

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  2. Winfried Sickel

    1. Institute of Mathematics, Friedrich-Schiller-University of Jena, Jena, Germany

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  3. Dachun Yang

    1. School of Mathematical Sciences, Beijing Normal University, Beijing, China, People's Republic

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  • 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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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 1-19

  3. The Spaces \(B_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) and \(F_{p, q}^{s, \tau }({\mathbb{R}}^ n)\)

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 21-48

  4. Almost Diagonal Operators and Atomic and Molecular Decompositions

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 49-64

  5. Several Equivalent Characterizations

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 65-135

  6. Pseudo-Differential Operators

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 137-146

  7. Key Theorems

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 147-175

  8. Inhomogeneous Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 177-250

  9. Homogeneous Spaces

    • Wen Yuan, Winfried Sickel, Dachun Yang
    Pages 251-269

  10. Back Matter

    Pages 271-288
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Keywords

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 = ∞.

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

  • School of Mathematical Sciences, Beijing Normal University, Beijing, China, People's Republic

    Wen Yuan, Dachun Yang

  • Institute of Mathematics, Friedrich-Schiller-University of Jena, Jena, Germany

    Winfried Sickel

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