A general theorem for absolute Cesàro summability of a series associated with a Fourier series

1964 ◽  
Vol 13 (3) ◽  
pp. 378-382 ◽  
Author(s):  
S. M. Mazhar
Keyword(s):  
Fourier Series ◽  
General Theorem ◽  
Cesàro Summability ◽  
Cesaro Summability

scholarly journals Lebesgue points of $$\ell _1$$-Cesàro summability of d-dimensional Fourier series

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Lebesgue Point ◽  
Cesàro Means ◽  
Cesàro Summability ◽  
Cesaro Means ◽  
Cesaro Summability ◽  
Lebesgue Points ◽  
Cesáro Means

AbstractWe generalize the classical Lebesgue’s theorem and prove that the $$\ell _1$$ ℓ 1 -Cesàro means of the Fourier series of the multi-dimensional function $$f\in L_1({{\mathbb {T}}}^d)$$ f ∈ L 1 ( T d ) converge to f at each strong $$\omega $$ ω -Lebesgue point.

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