Bernstein-Jackson-type inequalities with exact constants in Orlicz spaces

Abstract

We establish the Bernstein and Jackson type inequalities with exact constants for estimations of best approximations by exponential type functions in Orlicz spaces LM(Rn). For this purpose, we use a special scale of approximation spaces Bsτ (M) that are interpolation spaces between the subspace EM of exponential type functions and the space LM(Rn). These approximation spaces are defined using a functional E (t, f ) that plays a similar role as the module of smoothness. The constants in obtained inequalities are expressed using a normalization factor Nϑ,q that is determined by the parameters τ and s of the approximation space Bsτ (M).