Abstract
The aim of this paper is to prove the a.e. convergence of sequences of the Fejer means of the Walsh–Fourier series of bivariate integrable functions. That is, let \(a = (a_{1}, a_{2})\:\mathbb{N} \to \mathbb{N}^{2}\) such that a j (n+1)≧δsup k≦n a j (n) (j=1,2, n∈ℕ) for some δ>0 and a 1(+∞)=a 2(+∞)=+∞. Then for each integrable function f∈L 1(I 2) we have the a.e. relation \(\lim_{n\to\infty}\sigma_{a_{1}(n), a_{2}(n)}f = f\). It will be a straightforward and easy consequence of this result the cone restricted a.e. convergence of the two-dimensional Walsh–Fejer means of integrable functions which was proved earlier by the author and Weisz [3,8].
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