Pointwise strong (H, Phi) approximation by Fourier series of L^Psi integrable functions

2019/04/23 by Lenski, Wlodzimierz
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.10515

Abstract

We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H; Phi) as an approximation version of the Totik type generalization of the result of G. H. Hardy, J. E. Littlewood, in case of integrable functions from L^Psi. As a measure of such approximation we will use the function constructed by function Psi complementary to Phi on the base of defnition of the L^Psi points. Some corollary and remarks will also be given.

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