Abstract
We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the estimates obtained are unimprovable on some important functional subsets.
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Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 798–808, June, 2000
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Stepanets, A.I., Serdyuk, A.S. Lebesgue inequalities for poisson integrals. Ukr Math J 52, 914–925 (2000). https://doi.org/10.1007/BF02591785
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DOI: https://doi.org/10.1007/BF02591785