Equivalent norms in spaces of functions of fractional smoothness on an arbitrary domain. (Q1889540)

The paper deals with spaces of type \(B^s_{pq} (G)\) and \(F^s_{pq}(G)\) for arbitrary domains \(G \subset \mathbb{R}^n\) where \(s>0\), \(1\leq p,q \leq \infty\). The author proves that these spaces can be equivalently normed either in terms of means of differences or in terms of best polynomial approximations.