On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative

Abstract

A new non-periodic modulus of smoothness related to the Riesz derivative is constructed. Its properties are studied in the spaces L_p(ℝ) of non-periodic functions with 1 ≤ p ≤ +∞. The direct Jackson type estimate is proved. It is shown that the introduced modulus is equivalent to the K-functional related to the Riesz derivative and to the approximation error of the convolution integrals generated by the Fejér kernel.