2016; Physical and Mathematical Sciences, 50(1 (239): 64–66
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ON THE ALMOST EVERYWHERE CONVERGENCE OF NEGATIVE ORDER CESARO MEANS OF FOURIER–WALSH SERIES

Levon Galoyan*, R.G. Melibekyan

Received: 2025-02-11 · Published: 2016-03-18

© 2016 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON THE ALMOST EVERYWHERE CONVERGENCE OF NEGATIVE ORDER CESARO MEANS OF FOURIER–WALSH SERIES
Authors
Levon Galoyan, R.G. Melibekyan
Published
2016-03-18
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PSYU:A/2016.50.1.064

Abstract

In the paper is presented existence of an increasing sequence of natural numbers Mν,ν=0,1,..., such that for any ε>0 there exists a measurable set E with a measure μE>1−ε, such that for any function f∈L1[0,1] one can find a function g∈L1[0,1], which coincides with the function f on E, and for any α≠−1,−2,... the Cesaro means σMνα(x,f~), ν=0,1,..., converges to g(x) almost everywhere on [0,1].
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