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.
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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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DOI: https://doi.org/10.1007/978-3-642-14606-0_6
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14605-3
Online ISBN: 978-3-642-14606-0
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