Decompositions of function spaces.(English)Zbl 0920.46027

Escher, Joachim (ed.) et al., Topics in nonlinear analysis. The Herbert Amann anniversary volume. Basel: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 35, 691-730 (1999).
Today the theory of $$F^s_{pq}(\mathbb{R}^n)$$ spaces is well developed. It is the main aim of this paper to develop a corresponding intrinsic theory of $$F^s_{pq}(\Omega)$$ spaces, together with refined localizations, atomic and subatomic decompositions and with embeddings between weighted and unweighted spaces on $$\Omega$$. Here $$\Omega$$ is a bounded smooth domain in $$\mathbb{R}^n$$.
For the entire collection see [Zbl 0903.00112].
Reviewer: Josef Wloka (Kiel)

MSC:

 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems