Sharp Ul'yanov type inequalities in Lebesgue spaces

יום ב', 03/03/2014 - 14:00

We present sharp Ul’yanov type inequalities for fractional moduli of smoothness and K-functionals for the values of the parameters: 0<p<1, p<q. We also provide a generalization of Kolyada's inequality and relations between fractional moduli of smoothness of a function and  its derivatives in the spaces L_p, 0<p<1.