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.