Lebesgue inequalities for poisson integrals

@article{Stepanets2000LebesgueIF,
  title={Lebesgue inequalities for poisson integrals},
  author={A. I. Stepanets and A. Serdyuk},
  journal={Ukrainian Mathematical Journal},
  year={2000},
  volume={52},
  pages={914-925}
}
We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceLp,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofLp. We show that the estimates obtained are unimprovable on some important functional subsets. 
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Lebesgue's inequality on classes of (ψ, Β)-differentiable functions
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