Approximation by Abel — Poisson and conjugate Abel — Poisson means in seminormed spaces

Abstract

In this paper we establish the degree of approximation of a periodic function by the Abel — Poisson means of its Fourier series in a seminormed space. In addition, the corresponding problem for the conjugate function, approximated by the conjugate Abel — Poisson means of the conjugate Fourier series, is considered. Several corollaries of the main results are derived as special cases.