Geodesic
On sets of absolute convergence for multiple trigonometric series
Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 625-635.

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We obtain a sufficient condition for a set of measure zero in $N$-dimensional space to be a set of absolute convergence (A. C. set) for an $N$-tuple trigonometric series. We also show that, in a certain subclass of sets of measure zero (namely in the subclass of ldquo monotonicrdquo curves), this condition cannot be sharpened. 
@article{MZM_1973_13_5_a0,
     author = {R. A. Avetisyan},
     title = {On sets of absolute convergence for multiple trigonometric series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {625--635},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a0/}
}
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R. A. Avetisyan. On sets of absolute convergence for multiple trigonometric series. Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 625-635. http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a0/