cesaro means
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Author(s):  
György Gát ◽  
Ushangi Goginava

AbstractIn the present paper, we prove the almost everywhere convergence and divergence of subsequences of Cesàro means with zero tending parameters of Walsh–Fourier series.


2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Ferenc Weisz

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.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Samy A. Harisa ◽  
M. A. A. Khan ◽  
F. Mumtaz ◽  
Nashat Faried ◽  
Ahmed Morsy ◽  
...  

2020 ◽  
Vol 72 (3) ◽  
pp. 391-406
Author(s):  
T. Tepnadze

UDC 517.5 We establish approximation properties of Ces\`{a}ro means with α , β ϵ ( 0,1 ) of Vilenkin\,--\,Fourier series. This result allows one to obtain a condition which is sufficient for the convergence of the means σ n , m - α , - β ( x , y , f ) to f ( x , y ) in the L p -metric.


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