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

Anatoly Serdyuk; Tetiana Stepaniuk

doi:10.26485/0459-6854/2018/68.2/4

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

Anatoly Serdyuk, Tetiana Stepaniuk

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	45-52
Journal	Bulletin de la Société des Sciences et des lettres de Łódź: Série Recherches sur les Déformations
Volume	68
Issue number	2
DOIs	https://doi.org/10.26485/0459-6854/2018/68.2/4
Publication status	Published - 2018

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10.26485/0459-6854/2018/68.2/4Licence: CC BY-NC-ND 4.0

Bulletin-68-2-45-52Final published version, 343 KBLicence: CC BY-NC-ND 4.0

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title = "Lebesque-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.",

author = "Anatoly Serdyuk and Tetiana Stepaniuk",

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AU - Stepaniuk, Tetiana

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AB - 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.

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EP - 52

JO - Bulletin de la Société des Sciences et des lettres de Łódź: Série Recherches sur les Déformations

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

Abstract

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