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.
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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/

[1] Hörmander L., “Estimates for translation invariant operators in $L_p$ spaces”, Acta math., 104 (1960), 93–140 | DOI | MR | Zbl

[2] Brillhart J., Carlitz L., “Note on the Shapiro polynomials”, Proc. Amer. Math. Soc., 25 (1970), 114–118 | DOI | MR | Zbl

[3] Nursultanov E. D., “O multiplikatorakh ryadov Fure po trigonometricheskoi sisteme”, Mat. zametki, 63:2 (1998), 235–247 | MR | Zbl

[4] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973, 342 pp. | MR

[5] Nursultanov E. D., “Interpolation properties of some anisotropic spaces and Hardy–Littlewood type inequalities”, East J. Approx., 4:2 (1998), 243–275 | MR

[6] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR