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Walsh-Lebesgue points of multi-dimensional functions

О точках Уолща-Лебега функций нескольких переменных

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Abstract

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 i1 [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 i1 [0, 1)d is Fejér summable at each Walsh-Lebesgue point. Similar theorem is verified for ϑ-summability.

Резюме

В работе вводится понятие точек Уолща-Лебега для функций нескольких переменных. Доказано, что почти каждая точка является точкой Уолща-Лебега для функции из пространства Харди H i1 [0, 1)d, где

Всякая функция f из класса H i1 [0, 1)d суммируема по Фейеру в любой точке Уолща-Лебега. Аналогичный результат установлен для θ-суммируемости.

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Authors and Affiliations

  1. Department of Numerical Analysis, Eötvös L. University, 1117 Budapest, Pázmány P. sétány 1/C, Budapest, Hungary

    Ferenc Weisz

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  1. Ferenc Weisz
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Correspondence to Ferenc Weisz.

Additional information

This research was supported by the Hungarian Scientific Research Funds (OTKA) under Grant K 67 642.

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Weisz, F. Walsh-Lebesgue points of multi-dimensional functions. Anal Math 34, 307–324 (2008). https://doi.org/10.1007/s10476-008-0404-2

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  • DOI: https://doi.org/10.1007/s10476-008-0404-2

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