Decompositions of function spaces. (English) Zbl 0920.46027

Triebel, Hans

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:

46E35

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

Keywords:

localizations; atomic and subatomic decompositions; embeddings between weighted and unweighted spaces; smooth domain