Direct and inverse theorems on approximation of functions defined on a sphere in the space S ( p,q )(σm)

摘要

We prove direct and inverse theorems on the approximation of functions defined on a sphere in the space S (p,q)(σm), m ≥ 3, in terms of the best approximations and moduli of continuity. We consider constructive characteristics of functional classes defined by majorants of the moduli of continuity of their elements.