Abstract
An inequality of P. L. Ul’yanov connecting smoothness moduli of periodic functions in different metrics is refined in the paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. L. Ul’yanov, “The Embedding of Certain Function Classes H ωp ,” Izv. Akad. Nauk SSSR, Ser. Matem. 32(3), 649 (1968) [Math. of the USSR-Izvestiya 2 (3), 601 (1968)].
P. L. Ul’yanov, “Embedding Theorems and Relations Between Best Approximations (Moduli of Continuity) in Different Metrics,” Matem. Sborn. 81(123)(1), 104 (1970) [Math. of the USSR-Sbornik, 10 (1), 103 (1970)].
V. I. Kolyada, “Relations Between Continuity Moduli in Different Metrics,” Trudy Matem. Inst. Akad. Nauk. SSSR 181, 117 (1988).
A. Zygmund, Trigonometric Series, Vol. 2 (Cambridge Univ. Press, 1959; Mir, Moscow, 1965).
M. K. Potapov and B. V. Simonov, “On Interrelation of the Generalized Besov-Nikol’skii and Veyl-Nikol’skii Classes of Functions,” Anal. Math. 22, 299 (1996).
S. M. Nikol’skii, Approximation of Functions of Several Variables and the Embedding Theorems (Nauka, Moscow, 1977, Springer, Berlin, 1975).
Author information
Authors and Affiliations
Additional information
Original Russian Text © M.K. Potapov, B.V. Simonov, and S.Yu. Tikhonov, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008, Vol. 63, No. 3, pp. 33–36.
About this article
Cite this article
Potapov, M.K., Simonov, B.V. & Tikhonov, S.Y. An inequality of P. L. Ul’yanov. Moscow Univ. Math. Bull. 63, 115–118 (2008). https://doi.org/10.3103/S0027132208030078
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0027132208030078