Asymptotically best possible Lebesgue-type inequalities for the fourier sums on sets of generalized poisson integrals

Abstract

In this paper we establish Lebesgue-type inequalities for 2?-periodic functions f, which are defined by generalized Poisson integrals of the functions ? from Lp, 1 ? p < 1. In these inequalities uniform norms of deviations of Fourier sums ||f-Sn-1||C are expressed via best approximations En(?)Lp of functions ? by trigonometric polynomials in the metric of space Lp. We show that obtained estimates are asymptotically best possible.