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

Abstract: For functions from the set of generalized Poisson integrals $C^{\alpha,r}{\beta}L{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the generalized derivatives $f^{\alpha,r}_{\beta}$ of functions of this kind by trigonometric polynomials in the metric of the spaces $L_{p}$. Obtained estimates are asymptotically best possible.