Asymptotically best possible Lebesgue-type inequalities for the Fourier sums on sets of generalized Poisson integrals


Anatoly Serdyuk, Tetiana Stepanyuk




In this paper we establish Lebesgue-type inequalities for 2π-periodic functions f , which are defined by generalized Poisson integrals of the functions ϕ from L p , 1 ≤ p < ∞. In these inequalities uniform norms of deviations of Fourier sums f − S n−1 C are expressed via best approximations E n (ϕ) Lp of functions ϕ by trigonometric polynomials in the metric of space L p. We show that obtained estimates are asymptotically best possible