Morrey and Campanato Meet Besov, Lizorkin and Triebel

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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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 = ∞.

• 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

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)

• 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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