Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series (Q901310)

In this paper the strong summability result is proved for the quadratic partial sums of the two-dimensional Walsh-Fourier series. More exactly, it is shown that \[ \lim_{n\to\infty} \frac{1}{n} \sum_{k=0}^{n-1} | s_{k,k}f-f| ^q =0 \] almost everywhere, where \(f\in L\log L[0,1)^2\), \(q>0\) and \(s_{k,k}\) denote the quadratic partial sums of the Walsh-Fourier series of \(f\).