Geodesic
On the geometry of measurable sets in $N$-dimensional space on which generalized localization holds for multiple trigonometric Fourier series of functions from $L_p$, $p>1$
Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 87-109 
I. L. Bloshanskii. On the geometry of measurable sets in $N$-dimensional space on which generalized localization holds for multiple trigonometric Fourier series of functions from $L_p$, $p>1$. Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 87-109. http://geodesic.mathdoc.fr/item/SM_1984_49_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The precise geometry is found of measurable sets in $N$-dimensional Euclidean space on which generalized localization almost everywhere holds for multiple Fourier series which are rectangularly summable. Bibliography: 14 titles.

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[2] Bloshanskii I. L., “Generalized localization and convergence tests for double trigonometric Fourier series of functions from $L_p$, $p > l$”, Analysis Math., 7:1 (1981), 3–36 | DOI | MR

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[9] Bloshanskii I. L., “O ravnoskhodimosti razlozhenii v kratnyi trigonometricheskii ryad Fure i integral Fure”, Matem. zametki, 18:2 (1975), 153–168

[10] Tonelli L., Serie trigonometriche, Bologna, 1928

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[13] Whitney H., “Analytic extensions of differentiable functions defined in closed sets”, Trans. Amer. Math. Soc., 36 (1934), 63–89 | DOI | MR | Zbl

[14] Fefferman C., “On the divergence of multiple Fourier series”, Bull. Amer. Math. Soc., 77:2 (1971), 191–195 | DOI | MR | Zbl