Improvement of the Ul'yanov inequality for mixed moduli of smoothness for functions with lacunary Fourier coefficients}  / M. K. Potapov, B.  Simonov. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. ? 1. P. 18-24 [Moscow Univ. Math. Bulletin. Vol. 67, N 1, 2012.].

An inequality for the mixed moduli of smoothness for functions with lacunary Fourier coefficients improving the known Ul'yanov's inequality for moduli of smoothness is obtained in the paper.

Key words: mixed module of smoothness, lacunary Fourier coefficients, Ul'yanov's inequality.