Almost everywhere convergence of Cesàro means of two variable Walsh – Fourier series with varying parameteres
Abstract
UDC 517.5
We prove that the maximal operator of some $(C , \beta_{n})$ means of cubical partial sums of two variable Walsh – Fourier series of integrable functions is of weak type $(L_1,L_1)$. Moreover, the $ (C , \beta_{n})$-means $\sigma_{2^n}^{\beta_{n}} f$ of the function $ f \in L_{1} $ converge a.e. to $f$ for $ f \in L_{1}(I^2) $, where $I$ is the Walsh group for some sequences $1> \beta_n\searrow 0$.
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