Lebesgue-type inequalities for the Fourier sums on classes of generalized Poisson integrals

Abstract

For functions from the set of generalized Poisson integrals  , we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the generalized derivatives  of functions of this kind by trigonometric polynomials in the metric of the spaces . Obtained estimates are asymptotically best possible.