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Key Theorems

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

Abstract

In this chapter we focus on some crucial problems including pointwise multipliers, diffeomorphisms and traces, which govern the theory of the spaces \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) to a large extent. These problems are of vital importance both for function spaces treated for their own sake and for applications to partial differential equations. Following Triebel’s monograph [146], we call these assertions key theorems, since these theorems are the basis for the definitions of Besov-type spaces and Triebel-Lizorkin-type spaces on domains. An important tool used in this chapter is the smooth atomic decomposition characterization of \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) in Theorem 3.3.

Keywords

  • Besov Space
  • Smooth Domain
  • Dyadic Cube
  • Pointwise Multiplication
  • Isomorphic Mapping

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Dachun Yang .

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© 2011 Springer-Verlag Berlin Heidelberg

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Yuan, W., Sickel, W., Yang, D. (2011). Key Theorems. In: Morrey and Campanato Meet Besov, Lizorkin and Triebel. Lecture Notes in Mathematics(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14606-0_6

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