On the approximation properties of Cesa`ro means of negative order of Vilenkin-Fourier series

Author: Tsitsino Tepnadze
Keywords: Vilenkin System, Cesaro means
Annotation:

We establish approximation properties of Cesaro means(C,-α), α∈(0,1) with of Vilenkin-Fourier series (for two dimensional case we establish (C,-α,-β), α,β∈(0,1) means). This result allows one to obtain a condition which is sufficient for the convergence of the means σ_n^(-α) (f) to f in the L^p metric (for two dimensional case we have convergence of the means σ_(n,m)^(-α,-β) (f) to f ).

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ვილენკინ-ფურიეს მწკრივების ჩეზაროს უარყოფითი რიგის საშუალოების ნორმით კრებადობა [ka]