Strengthened Ul’yanov’s Inequalities for Partial Moduli of Smoothness for Functions from Spaces with Various Metrics
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Ul’yanovs inequality connecting moduli of continuity in different metrics is well known for functions of one variable. In this paper functions of two variables are considered. Sharp Ul’yanov’s inequalities connecting partial moduli of smoothness of positive order are proved in different mixed metrics.
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- 1.P. L. Ul’yanov, “Embedding Theorems and Relations Between the Best Approximations (Moduli of Continuity) in Different Metrics,” Matem. Sbornik 81(123)(1), 104 (1970).Google Scholar
- 2.M. K. Potapov and B. V. Simonov, “Relations Between Moduli of Smoothness in Different Metrics,” Vestn. Mosk. Univ., Matem. Mekhan., No 3, 17 (2009).Google Scholar
- 4.M. K. Potapov and B. V. Simonov, “Full Moduli of Smoothness of Positive Orders for Functions from L p, 1 < p < ∞, Spaces,” in Modern Problems of Mathematics and Mechanics. Proc. Mech. Math. Faculty of Moscow State Univ. Vol. X: Mathematics. Issue 2 (to 100th anniversary of Luzin’s seminar on the theory of functions.) (Moscow State Univ., Moscow, 2015), pp. 101–133.Google Scholar
- 7.M. K. Potapov and B. V. Simonov, “Properties of the Partial Modulus of Smoothness of Positive Order in a Mixed Metric,” in Modern Problems of Mathematics and Mechanics. Proc. Mech. Math. Faculty of Moscow State Univ. Vol. X: Mathematics. Issue 1 (to 60th anniversary of the seminar “Trigonometric and Orthogonal Series.”) (Moscow State Univ., Moscow, 2014), pp. 58–70.Google Scholar
- 8.M. K. Potapov and B. V. Simonov, “Inequalities of Different Metrics for Trigonometric Polynomials,” Izvestiay Vyzov, Matem., No 1, 49, (2019).Google Scholar
- 9.A. P. Uninskii, “Inequalities in a Mixed Norm for Trigonometric Polynomials and Entire Functions of Finite Degree,” in Proc. All-Union Symp. on Embedding Theorems. Baku, 1966, pp 212–213.Google Scholar
- 10.M. K. Potapov, B. V. Simonov, and S. Yu. Tikhonov, Fractional Moduli of Smoothness. (MAKS Press, Moscow, 2016) [in Russian].Google Scholar