Geodesic
Multipliers of Multiple Fourier Series
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Investigations in the theory of differentiable functions of many variables and its applications. Part 18, Tome 227 (1999), pp. 237-242

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In this paper, multipliers of multiple trigonometric Fourier series are studied; upper and lower estimates for the norm of these multipliers are proved; and the exactness of these estimates is shown on certain classes. 
@article{TM_1999_227_a16,
     author = {E. D. Nursultanov and N. T. Tleukhanova},
     title = {Multipliers of {Multiple} {Fourier} {Series}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {237--242},
     publisher = {mathdoc},
     volume = {227},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1999_227_a16/}
}
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E. D. Nursultanov; N. T. Tleukhanova. Multipliers of Multiple Fourier Series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Investigations in the theory of differentiable functions of many variables and its applications. Part 18, Tome 227 (1999), pp. 237-242. http://geodesic.mathdoc.fr/item/TM_1999_227_a16/