Geodesic
Convergence of Double Cosine Series
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 3, p. 443 .

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In this paper we consider double cosine series whose coefficients form a null sequence of bounded variation of order $(p, 0)$, $(0, p)$ and $(p, p)$ with the weight $(jk)^{p-1}$ for some $p> 1$. We study pointwise convergence, uniform convergence and convergence in $L^r$-norm of the series under consideration. In a certain sense our results extend the results of Young \cite{Young}, Kolmogorov \cite{Kolmogorov} and Móricz \cite{Moricz1,Moricz2}.
Classification : 42A20, 42A32
Keywords: Rectangular partial sums, $L^r-$convergence, $Ces\gravearo $ means, monotone sequences 
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     author = {Karanvir Singh and Kanak Modi},
     title = {Convergence of {Double} {Cosine} {Series}},
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Karanvir Singh; Kanak Modi. Convergence of Double Cosine Series. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 3, p. 443 . http://geodesic.mathdoc.fr/item/KJM_2020_44_3_a9/