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Approximation of classes of analytic functions by Fourier sums in the metric of the space L p

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Abstract

We establish asymptotic equalities for upper bounds of approximations by partial Fourier sums in the metrics of the spaces L p , 1 ≤ p ≤ ∞, on classes of Poisson integrals of periodic functions belonging to the unit ball of the space L 1. The results obtained are generalized to the classes of \((\psi ,\bar \beta )\)-differentiable (in the sense of Stepanets) functions that admit an analytic extension to a fixed strip of the complex plane.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    A. S. Serdyuk

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  1. A. S. Serdyuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1395–1408, October, 2005.

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Serdyuk, A.S. Approximation of classes of analytic functions by Fourier sums in the metric of the space L p . Ukr Math J 57, 1635–1651 (2005). https://doi.org/10.1007/s11253-006-0018-4

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  • DOI: https://doi.org/10.1007/s11253-006-0018-4

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