Ul'anov type inequalities for moduli of smoothness

Abstract

Let T denote the interval [-?, ?]. In this work we investigate the inequality of Ul'yanov type for moduli of smoothness of an integer order in the Lp (T), p ? 1 spaces. In particular, we study (p, q) inequalities for moduli of smoothness of a derivative of a function via the modulus of smoothness of the function itself.