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

For functions from the set of generalized Poisson integrals $C_{\beta }^{\alpha ,r}{L}_p$, $1\le p<\mathrm{\infty }$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the generalized derivatives $f_{\beta }^{\alpha ,r}$ of functions of this kind by trigonometric polynomials in the metric of the spaces $L_p$. Obtained estimates are asymptotically best possible.