ON THE ALMOST EVERYWHERE CONVERGENCE OF NEGATIVE ORDER CESARO MEANS OF FOURIER–WALSH SERIES

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Submitted: 2025-02-11; Published: 2025-02-11

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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].