English

Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals

Classical Analysis and ODEs 2018-04-17 v1

Abstract

For functions from the set of generalized Poisson integrals Cβα,rLpC^{\alpha,r}_{\beta}L_{p}, 1p<1\leq p <\infty, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the generalized derivatives fβα,rf^{\alpha,r}_{\beta} of functions of this kind by trigonometric polynomials in the metric of the spaces LpL_{p}. Obtained estimates are asymptotically best possible.

Keywords

Cite

@article{arxiv.1804.05722,
  title  = {Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals},
  author = {Anatoly Serdyuk and Tetiana Stepaniuk},
  journal= {arXiv preprint arXiv:1804.05722},
  year   = {2018}
}