- Constructive Mathematical Analysis
- Volume: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 WEİSZ
Pages : 179-185
Doi:10.33205/cma.859583
View : 12 | Download : 5
Publication Date : 2021-06-01
Article Type : Research Paper
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_1insert ignore into journalissuearticles values(\log L);^{d-1}insert ignore into journalissuearticles values(\mathbb{T}^d);\supset L_pinsert ignore into journalissuearticles values(\mathbb{T}^d); insert ignore into journalissuearticles values(1
Keywords : Cesàro summability, strong Hardy Littlewood maximal function, strong Lebesgue points