One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables

Abstract

We obtain a new sharp inequality of the Landau–Kolmogorov type for a periodic function of two variables estimating the convolution of the best uniform approximations of its partial primitives by the sums of functions of single variable via the L∞-norm of the function itself and uniform norms of its mixed primitives. Some applications of the obtained inequality are also presented.