Intrinsic atomic characterizations of function spaces on domains (Q1906894)

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.