Strengthened Ul'yanov's Inequality for Complete Moduli of Smoothness of Functions from Spaces with Mixed Metrics / *M. K. Potapov and B. V. Simonov.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. № 6. P. 8-20
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 217-228].

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.

*Key words*:
inequality, full modulus of smoothness, mixed metric.