Limits of Besov norms

Besov spaces \({{\mathbf B}^s_{p,q} ({\mathbb R}^n)}\) with s > 0 can be normed in terms of the differences \({\Delta^m_h f}\) and related moduli of smoothness ω _m (f, t) _p , where \({0 < s < m \in {\mathbb N}}\). The paper deals with the question what happens if \({s {\uparrow} m}\) and how the outcome is related to the Sobolev spaces \({{\mathbf W}^m_p ({\mathbb R}^n)}\).