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

Anatoly Serdyuk; Tetiana Stepaniuk

paper

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

arXiv:1804.05722

Abstract

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