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

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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

Pages : 179-185

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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

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