Abstract
A class of functions generalizing well-known Nikol’skii classes is considered. An embedding theorem of different metrics is proved.
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References
S. M. Nikol’skii, “Functions with Dominant Mixed Derivative Satisfying a Multiple Holder Condition,” Sib. Matem. Zh. 4 (6), 1342 (1963).
S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems (Nauka, Moscow, 1977; Springer-Verlag, N.Y., 1975).
P. I. Lizorkin and S. M. Nikol’skii, “Classification of Differentiable Functions on the Basis of Spaces with Dominant Mixed Derivatives,” Trudy Steklov Matem. Inst. 77, 143 (1965).
M. K. Potapov, “On Approximation by Angle,” in: Proc. Gonf. Constructive Theory of Functions (Approximation Theory). 1969, Ed. by G. Alexits and S. B. Stechkin (Akad. Kiado, Budapest, 1972), pp. 371–399.
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Original Russian Text © T. F. Ismagilou. 2015. published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2015, Vol. 70, No. 4, pp. 28-32.
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Ismagilov, T.F. Embedding theorem of different metrics for a generalized Nikol'skii class. Moscow Univ. Math. Bull. 70, 176–180 (2015). https://doi.org/10.3103/S002713221504004X
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DOI: https://doi.org/10.3103/S002713221504004X