Spaces of functions of fractional smoothness on an irregular domain. (Q1889524)

Let \(G\) be an arbitrary domain in \(\mathbb{R}^n\). The paper deals with spaces of type \(B^s_{pq} (G)\), \(F^s_{pq} (G)\), where \(s>0\), \(1\leq p,q \leq \infty\), are characterised by integral representations, norms in terms of differences, and (equivalently) in terms of best approximations by polynomials. The main aim of this paper is to study the embedding \[ B^s_{pp} (G) \hookrightarrow L_q (G), \quad 1<p<q< \infty, \] subject to the quality of the irregular domain \(G\).