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Literature Cited
N. S. Nikol'skaya, “The approximation of differetiable functions of several variables by Fourier sums in the metric of hp,” Dokl. Akad. Nauk SSSR,208, No. 6, 1282–1285 (1973).
K. I. Babenko, “The approximation of periodic functions of several variables by trigonometric polynomials,” Dokl. Akad. Nauk SSSR,132, No. 2, 247–250 (1960).
K. I. Babenko, “The approximation of a class of periodic functions of several variables by trigonometric polynomials,” Dokl. Akad. Nauk SSSR,132, No. 5, 982–985 (1960).
B. S. Mityagin, “The approximation of functions in the space hp and C on a torus,” Matem. Sb.,58, No. 4, 397–414 (1962).
S. A. Telyakovskii, “Estimates of the derivatives of trigonometric polynomials of several variables,” Sibirsk. Matem. Zh.,IV, No. 6, 1404–1414 (1963).
Ya. S. Bugrov, “The approximation of a class of functions with a dominant mixed derivative,” Matem. Sb.,64, No. 3, 410–418 (1964).
A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge (1968).
P. I. Lizorkin, “The Fourier transformation in Besov spaces. The zero scale B0 pθ,” Dokl. Akad. Nauk, SSSR,163, No. 6, 1318–1321 (1965).
J. Marcinkiewicz, “Sur les multiplicateurs des series de Fourier,” Studia Math.,8, 78–91 (1939).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 2, pp. 395–412, March–April, 1974.
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Nikol'skaya, N.S. The approximation in the Lp metric of differentiable functions of several variables by Fourier sums. Sib Math J 15, 282–295 (1974). https://doi.org/10.1007/BF00968291
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DOI: https://doi.org/10.1007/BF00968291