Lebesgue inequalities for poisson integrals - Serdyuk, A. S.; Stepanets, O. I. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the estimates obtained are unimprovable on some important functional subsets.