Kolmogorov type inequalities for functions analytic in circle

Abstract

In the paper we obtain a series of Kolmogorov type inequalities for functions analytic in a circle of an arbitrary radius $R$ and belonging to the Hardy space $H_{q,R}$ $(1\leq
q\leq\infty,\,R>0)$. We provide some applications of these inequalities in extremal problem of best polynomial approximation.