Bernstein-Jackson-type inequalities with exact constants in Orlicz spaces - Dmytryshyn, M.I.; Dmytryshyn, L.I. (Carpathian Mathematical Publications, 2022)
We establish the Bernstein and Jackson type inequalities with exact constants for estimations of best approximations by exponential type functions in Orlicz spaces L_M(R^n). For this purpose, we use a special scale of approximation spaces B_τ^s(M) that are interpolation spaces between the subspace E_M of exponential type functions and the space L_M(R^n). 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 N_ϑ,q that is determined by the parameters τ and s of the approximation space B_τ^s(M).