Lebesgue-type inequalities for the de la Valée-Poussin sums on sets of analytic functions

  title={Lebesgue-type inequalities for the de la Val{\'e}e-Poussin sums on sets of analytic functions},
  author={A. Musienko and A. Serdyuk},
  journal={Ukrainian Mathematical Journal},
For functions from the sets CβψC and CβψLs, 1 ≤ s ≤ 1, generated by sequences ψ(k) > 0 satisfying the d’Alembert condition $ {\lim_{{k\to \infty }}}\frac{{\psi \left( {k+1} \right)}}{{\psi (k)}}=q,\;q\in \left( {0,1} \right) $, we obtain asymptotically sharp estimates for the deviations of de la Vallée-Poussin sums in the uniform metric 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… Expand
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