On the almost everywhere convergence of negative order Cesaro means of Fourier–Walsh series (Ֆուրիե–Ուոլշի շարքի Չեզարոյի բացասական կարգի միջինների զուգամիտության մասին)

Аннотация

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 ∈ L 1 [0,1] one can find a function g ∈ L 1 [0,1], which coincides with the function f on E, and for any α 6= −1,−2,... the Cesaro means σ α Mν (x, ˜f),ν = 0,1,..., converges to g(x) almost everywhere on [0,1].