Relations Between Moduli of Smoothness in Different Metrics / M.K. Potapov, B.V. Simonov, and S.Yu. Tikhonov // Vestn. Mosk. Univ., Matem. Mekhan. 2009. № 3. P. 17-25 [Moscow Univ. Math. Bulletin. Vol. 64, No 3, 2009. P. 105-112]
Two inequalities are proved in the paper. These inequalities extend and refine the well-known 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.