For the least upper bounds of deviations of the de la Vallée-Poussin operators on the classes \( \hat{L}_\beta^\psi \) of rapidly vanishing functions ψ in the metric of the spaces \( {\hat{L}_p} \), 1 ≤ p ≤ ∞, we establish upper estimates that are exact on some subsets of functions from \( {\hat{L}_p} \).
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V. I. Rukasov (Deceased).
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 968–978, July, 2010.
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Rukasov, V.I., Chaichenko, S.O. Approximation by de la Vallée-Poussin operators on the classes of functions locally summable on the real axis. Ukr Math J 62, 1126–1138 (2010). https://doi.org/10.1007/s11253-010-0418-3
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DOI: https://doi.org/10.1007/s11253-010-0418-3