Geodesic
Necessary and sufficient conditions for the $L^1$-convergence of double Fourier series
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 987-996.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the $L^1$-convergence of double Fourier series. We also give necessary and sufficient conditions for the $L^1$-convergence under appropriate assumptions.
DOI : 10.21136/CMJ.2018.0043-17
Classification : 42B05, 42B99
Keywords: double Fourier series; $L^1$-convergence; logarithm bound variation double sequences 
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     title = {Necessary and sufficient conditions for the $L^1$-convergence of double {Fourier} series},
     journal = {Czechoslovak Mathematical Journal},
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     publisher = {mathdoc},
     volume = {68},
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Kórus, Péter. Necessary and sufficient conditions for the $L^1$-convergence of double Fourier series. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 987-996. doi : 10.21136/CMJ.2018.0043-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0043-17/

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