Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space S^p - Serdyuk, A. S.; Stepanets, O. I. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We continue the investigation of approximation properties of the space S^p. We introduce the notion of kth modulus of continuity and establish direct and inverse theorems on approximation in the space S^p in terms of the best approximations and moduli of continuity. These theorems are analogous to the well-known theorems of Jackson and Bernshtein.