scholarly journals Fourier series, XIV. Order of approximation of partial sums and Cesàro means

1957 ◽  
Vol 33 (3) ◽  
pp. 114-118 ◽  
Author(s):  
Shin-ichi Izumi ◽  
Masako Satô ◽  
Gen-ichirô Sunouchi
Keyword(s):  
Fourier Series ◽  
Partial Sums ◽  
Cesàro Means ◽  
Order Of Approximation ◽  
Cesaro Means ◽  
Cesáro Means

Uniform summability of double Walsh-Fourier series of functions of bounded partial Λ-variation

2014 ◽  
Vol 64 (6) ◽  
Author(s):  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Uniformly Convergence ◽  
Negative Order ◽  
Cesáro Means ◽  
Sufficient And Necessary Conditions ◽  
Series Of Functions

AbstractThe sufficient and necessary conditions on the sequence Λ = {λn} are found for the uniformly convergence of Cesàro means of negative order of cubic partial sums of double Walsh-Fourier series of functions of bounded partial Λ-variation.

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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