Walsh-Lebesgue points of multi-dimensional functionsО точках Уолща-Лебега функций нескольких переменных

Walsh-Lebesgue points are introduced for higher dimensions and it is proved that a.e. point is a Walsh-Lebesgue point of a function f from the Hardy space H1i[0, 1)d, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H_1^i [0,1]^d \supset L(\log L)^{d - 1} [0,1)^d for all i = 1,...,d $$\end{document}. Every function f ∈ H1i[0, 1)d is Fejér summable at each Walsh-Lebesgue point. Similar theorem is verified for ϑ-summability.