Geodesic
On uniformly convergent double Fourier series
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 151-162

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The uniform convergence in question is defined by means of a system of mutually homotetic starlike polygons. It is established, among other things, that an arbitrary positive sequence in $l^2(\mathbb{T}^2)$ can be majorized by the sequence of absolute values of coefficients of a uniformly convergent double Fourier series. 
@article{ZNSL_1989_178_a6,
     author = {S. V. Kislyakov},
     title = {On uniformly convergent double {Fourier} series},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--162},
     publisher = {mathdoc},
     volume = {178},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a6/}
}
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S. V. Kislyakov. On uniformly convergent double Fourier series. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 151-162. http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a6/