Maximal operators of Cesàro means with varying parameters of Walsh–Fourier series

2019 ◽  
Vol 159 (2) ◽  
pp. 653-668 ◽  
Author(s):  
G. Gát ◽  
U. Goginava
Keyword(s):  
Fourier Series ◽  
Maximal Operators ◽  
Cesàro Means ◽  
Varying Parameters ◽  
Cesaro Means ◽  
Cesáro Means

scholarly journals Almost everywhere convergence and divergence of Cesàro means with varying parameters of Walsh–Fourier series

2021 ◽  
Author(s):  
György Gát ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Cesàro Means ◽  
Almost Everywhere Convergence ◽  
Varying Parameters ◽  
Cesaro Means ◽  
Almost Everywhere ◽  
Cesáro Means ◽  
Convergence And Divergence

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.

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.

scholarly journals On the convergence of Cesàro means of negative order of Vilenkin-Fourier series

2019 ◽  
Vol 56 (1) ◽  
pp. 22-44
Author(s):  
Gvantsa Shavardenidze
Keyword(s):  
Fourier Series ◽  
Continuous Function ◽  
Uniform Convergence ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Negative Order ◽  
Cesáro Means

Abstract In 1971 Onnewer and Waterman establish a sufficient condition which guarantees uniform convergence of Vilenkin-Fourier series of continuous function. In this paper we consider different classes of functions of generalized bounded oscillation and in the terms of these classes there are established sufficient conditions for uniform convergence of Cesàro means of negative order.

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