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arXiv · 1804.05722

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

Anatoly Serdyuk·Tetiana Stepaniuk
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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.

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BibTeXRIS

Anatoly Serdyuk, Tetiana Stepaniuk. 2018-04-16. Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals. https://arxiv.org/abs/1804.05722

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