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

  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},
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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