Relations between moduli of smoothness in different metrics / M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. ? 3. P. 17-25 [Moscow Univ. Math. Bulletin. Vol. 64, N 3, 2009. P. 105-112].

Two inequalities are proved in the paper. These inequalities extend and refine the well-known P.L. Yl'yanov's inequality concerning relations between moduli of continuity in various metrics.

Key words: modulus of smoothness, space metric, periodic function, accuracy of an inequality.