Walsh-Lebesgue points of multi-dimensional functions

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 H ₁ ⁱ 0, 1) ^d , where $$ H_1^i 0,1]^d \supset L(\log L)^{d - 1} 0,1)^d for all i = 1,...,d $$ . Every function f ∈ H ₁ ⁱ 0, 1) ^d is Fejér summable at each Walsh-Lebesgue point. Similar theorem is verified for ?-summability.