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Intrinsic atomic characterizations of function spaces on domains. (English) Zbl 0843.46022

The spaces \(B^s_{pq} (\Omega)\) and \(F^s_{pq} (\Omega)\) are defined by restriction of corresponding spaces on \(\mathbb{R}^n\), where \(\Omega\) is a (maybe rather nasty) domain in \(\mathbb{R}^n\). Here \(s\in \mathbb{R}\), \(0< p,q\leq \infty\) \((p< \infty\) in the \(F\)-case). The aim of the paper is to give an intrinsic atomic characterization of all these spaces.
Reviewer: H.Triebel (Jena)

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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