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Strengthened Ul’yanov’s Inequality for Complete Moduli of Smoothness of Functions from Spaces with Mixed Metrics

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Abstract

Ul’yanov’s inequality on the connection between moduli of continuity in different metrics is well known for functions of one variable. Functions of two variables are analyzed in this paper. The sharp Ul’yanov’s inequality for full moduli of smoothness of positive order in different mixed metrics is proved.

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Authors and Affiliations

  1. Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, 119991, Russia

    M. K. Potapov

  2. Volgograd State Technical University, 28 Lenin av., Volgograd, 400005, Russia

    B. V. Simonov

Authors
  1. M. K. Potapov
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  2. B. V. Simonov
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Corresponding authors

Correspondence to M. K. Potapov or B. V. Simonov.

Additional information

Original Russian Text © M.K. Potapov, B.V. Simonov, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 6, pp. 8–20.

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Potapov, M.K., Simonov, B.V. Strengthened Ul’yanov’s Inequality for Complete Moduli of Smoothness of Functions from Spaces with Mixed Metrics. Moscow Univ. Math. Bull. 73, 217–228 (2018). https://doi.org/10.3103/S0027132218060025

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