# Lebesgue-type inequalities for the de la Vallée-poussin sums on sets of entire functions

@article{Musienko2013LebesguetypeIF,
title={Lebesgue-type inequalities for the de la Vall{\'e}e-poussin sums on sets of entire functions},
author={A. Musienko and A. Serdyuk},
journal={Ukrainian Mathematical Journal},
year={2013},
volume={65},
pages={709-722}
}
• Published 2013
• Mathematics
• Ukrainian Mathematical Journal
For functions from the sets CψβLs, 1 ≤ s ≤ ∞, where ψ(k) > 0 and ${\lim_{{k\to \infty }}}\frac{{\psi \left( {k+1} \right)}}{{\psi (k)}}$, we obtain asymptotically sharp estimates for the norms of deviations of the de la Vallée-Poussin sums in the uniform metric represented in terms of the best approximations of the (ψ, β) -derivatives of functions of this kind by trigonometric polynomials in the metrics of the spaces Ls. It is shown that the obtained estimates are sharp on some important… Expand
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