Unrestricted Cesàro summability of $d$-dimensional Fourier series and Lebesgue points

Year 2021, Volume: 4 Issue: 2, 179 - 185, 01.06.2021

Ferenc Weisz

https://doi.org/10.33205/cma.859583

Cited By: 1

Abstract

We generalize the classical Lebesgue's theorem to multi-dimensional functions. We prove that the Cesàro means of the Fourier series of the multi-dimensional function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1<p<\infty)$ converge to $f$ at each strong Lebesgue point.

Keywords

Cesàro summability, strong Hardy-Littlewood maximal function, strong Lebesgue points

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