M. K. Potapov, B. V. Simonov, “Strengthened Ul'yanov's inequalities for partial moduli of smoothness for functions from spaces with various metrics”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, Number 3,Pages <nobr>26

This article is cited in 2 papers

Mathematics

Strengthened Ul'yanov's inequalities for partial moduli of smoothness for functions from spaces with various metrics

M. K. Potapov^a, B. V. Simonov^b

^a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Volgograd State Technical University

Abstract: Ul'yanov's 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.

Key words: inequality, partial modulus of smoothness, mixed metric.

UDC: 517.5

Received: 18.07.2018