Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $ {H_{{\omega_p}}} $ in the metrics of the spaces Lp

@article{Serdyuk2010LinearAM,
  title={Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes \$ \{H_\{\{\omega_p\}\}\} \$ in the metrics of the spaces Lp},
  author={A. Serdyuk and I. V. Sokolenko},
  journal={Ukrainian Mathematical Journal},
  year={2010},
  volume={62},
  pages={1139-1157}
}
We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from $ {H_{{\omega_p}}} $ for 1 ≤ p < ∞ by a certain linear method Un* in the metric of the space Lp. It is shown that the obtained estimates are asymptotically exact for p = 1: In addition, we determine the asymptotic equalities for the best approximations of the classes of Poisson integrals of functions from $ {H_{{\omega_1}}} $ in the metric of the space L1 and show that… Expand
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