Geodesic
Convergence of Double Fourier Series after a Change of Variable
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 267-277 
A. A. Sahakian. Convergence of Double Fourier Series after a Change of Variable. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 267-277. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a8/
@article{MZM_2003_74_2_a8,
     author = {A. A. Sahakian},
     title = {Convergence of {Double} {Fourier} {Series} after a {Change} of {Variable}},
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     year = {2003},
     volume = {74},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we prove that for any compact set $\Omega\subset C(\mathbb T^2)$ there exists a homeomorphism $\tau$ of the closed interval $\mathbb T=[-\pi,\pi]$ such that for an arbitrary function $f\in\Omega$ the Fourier series of the function $F(x,y)=f(\tau(x),\tau(y))$ converges uniformly on $C(\mathbb T^2)$ simultaneously over rectangles, over spheres, and over triangles.

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