On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions1

摘要

The paper is concerned with establishing direct estimates for convolution operators on homogeneous Banach spaces of periodic functions by means of appropriately defined K-functional. The differential operator in the K-functional is defined by means of strong limit and described explicitly in terms of its Fourier coefficients. The description is simple and independent of the homogeneous Banach space. Saturation of such operators is also considered.