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A high-indices theorem for strong Cesàro summability of double series

Одна теорема повышен ия индекса для сильно й суммируемости по Чезаро двойных ряд ов

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Abstract

В предшествующей раб оте [4] автор установил, что если двойной числовой ряд [C,(α, β)];-суммируем (α, β≧0 и λ≧1) к значениюs, т о он также [C,(α+δ,β+γ)]μ-суммируем кs для любого γ, δ≧0 и 0<μ≦λ В нас тоящей работе доказы вается, что если (i) α, β ≧; μ >λ > 1 и\(\delta ,\gamma \geqq \frac{1}{\lambda } - \frac{1}{\mu }\), или если (ii) α,β>0; μ>λ=1 и δ,γ>1-1/μ, то [C,(α,β)λ-сум мируемость влечет [C,(α+δ,β+γ)]μ-суммируемос ть.

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References

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Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi Vértanúk Tere 1, 6720, Szeged, Hungary

    I. Szalay

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  1. I. Szalay
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This work was done while the author was a visiting researcher at the Steklov Mathematical Institute, Moscow, U.S.S.R.

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Szalay, I. A high-indices theorem for strong Cesàro summability of double series. Analysis Mathematica 16, 65–80 (1990). https://doi.org/10.1007/BF01906774

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  • DOI: https://doi.org/10.1007/BF01906774

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