- Constructive Mathematical Analysis
- Vol: 4 Issue: 2
- Unrestricted Cesàro summability of $d$-dimensional Fourier series and Lebesgue points
Unrestricted Cesàro summability of $d$-dimensional Fourier series and Lebesgue points
Authors : Ferenc Weisz
Pages : 179-185
Doi:10.33205/cma.859583
View : 9 | Download : 6
Publication Date : 2021-06-01
Article Type : Research
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
Keywords : Cesàro summability, strong Hardy-Littlewood maximal function, strong Lebesgue points