Geodesic
Convergence of the Hausdorff Means ofDouble Fourier Series*
Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 585-591

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In this paper we prove that if {sm, n(x, y)} is the sequence of partial sums of the Fourier series of a function f(x, y), which is periodic in each variable and of bounded variation in the sense of Hardy-Krause in the period rectangle, then {sm, n(x, y)} converges uniformly to f(x, y) in any closed region D in which this function is continuous at every point. This result is then used to prove that the regular Hausdorff means of the Fourier series of such a function also converge uniformly in such a region. 
Ustina, Fred. Convergence of the Hausdorff Means ofDouble Fourier Series*. Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 585-591. doi: 10.4153/CMB-1968-070-5
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     author = {Ustina, Fred},
     title = {Convergence of the {Hausdorff} {Means} {ofDouble} {Fourier} {Series*}},
     journal = {Canadian mathematical bulletin},
     pages = {585--591},
     year = {1968},
     volume = {11},
     number = {4},
     doi = {10.4153/CMB-1968-070-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-070-5/}
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