Properties of Cesàro means of double Fourier series

2010 ◽  
Vol 65 (2) ◽  
pp. 55-62
Author(s):  
A. M. D’yachenko
Keyword(s):  
Fourier Series ◽  
Double Fourier Series ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Cesáro Means

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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