Geodesic
On Absolute Convergence of Multiple Fourier Series
Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 81-93.

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We obtain sufficient conditions for $\beta$-absolute convergence ($0\beta\leq 1$) of multiple Fourier series of functions of the classes $$ L^2([0,2\pi]^{N}),\qquad (\Lambda^{1},\Lambda^{2},\dots,\Lambda^{N})BV^{(p)}([0,2\pi]^{N}),\qquad r-BV([0,2\pi]^{N}). $$
Keywords: absolute convergence, multiple Fourier series, functions of $(\Lambda^{1},\Lambda^{2},\dots,\Lambda^{N})BV^{(p)}$ and $r-BV$. 
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R. G. Vyas; K. N. Darji. On Absolute Convergence of Multiple Fourier Series. Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 81-93. http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a6/

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