On simultaneous approximation of certain classes of functions in the Bergman space <i>B</i>₂

Abstract

The problem of finding the supremums of the best simultaneous polynomial approximations of some classes of functions analytic in the unit disk and belonging to the Bergman space B2 is considered. The indicated function classes are defined by the averaged values of the mth order moduli of continuity of the highest derivative bounded from above by some majorant Φ.