Direct and inverse theorems on approximation of functions defined on a sphere in the space <i>S </i>^(<i>p,q</i>)(σ^{<i> m</i>})

Abstract

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