The fundamental theorem of two-parameter pointwise derivative on Vilenkin groups (Q1125588)

It is proved on two-parameter bounded Vilenkin groups that the integral of a two-dimensional function \(f\in L_1\) is Vilenkin differentiable and its derivative is a.e. \(f\), if the limit in the derivative is taken in a cone. The same result for the two-parameter dyadic group was proved by \textit{F. Weisz} [Stud. Math. 120, No. 3, 271-288 (1996; Zbl 0860.42022)] and \textit{G. Gát} [J. Approximation Theory 92, No. 2, 191-215 (1998; Zbl 0897.42017)].