One inequality of the Landau – Kolmogorov type for periodic functions of two variable

Abstract

We obtain a new sharp inequality of the Landau – Kolmogorov type for a periodic function of two variables that estimates the convolution of the best uniform approximations of its partial primitives by the sums of univariate functions with the help of its $L_{\infty}$ -norm and uniform norms of its mixed primitives. Some applications of the obtained inequality are presented.