Geodesic
Uniform convergence of expansions into a~multiple trigonometric Fourier series or a~Fourier integral
Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 153-168.

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Questions of convergence almost everywhere of expansions into a multiple trigonometric Fourier series or a Fourier integral are studied for functions from $L_p$, $p\ge1$, with summation over rectangles. Moreover, a ldquogeneralized localization principle,rdquo understood in the sense of convergence almost everywhere, is considered in the paper. 
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     author = {I. L. Bloshanskii},
     title = {Uniform convergence of expansions into a~multiple trigonometric {Fourier} series or {a~Fourier} integral},
     journal = {Matemati\v{c}eskie zametki},
     pages = {153--168},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a0/}
}
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I. L. Bloshanskii. Uniform convergence of expansions into a~multiple trigonometric Fourier series or a~Fourier integral. Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 153-168. http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a0/