Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$
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.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 1, pp 126–148.
Citation Example: Serdyuk A. S., Stepanets O. I. Direct and Inverse Theorems in the Theory of Approximation of Functions in the Space $S^p$ // Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 106-124.