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 $r-BV$. 
@article{MZM_2013_94_1_a6,
     author = {R. G. Vyas and K. N. Darji},
     title = {On {Absolute} {Convergence} of {Multiple} {Fourier} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {81--93},
     publisher = {mathdoc},
     volume = {94},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a6/}
}
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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/