Jackson-stechkin type inequality in weighted lorentz spaces

Abstract

In the present work we consider the modulus of smoothness, defined by means of the Steklov operator in weighted Lorentz spaces and prove the Jackson-Stechkin type direct theorem of trigonometric approximation. In the particular case we obtain a result on the constructive characterization of the generalized Lipschitz classes defined in these spaces. Simultaneous approximation of functions is also considered.