Sharp constants of approximation theory. V. An asymptotic equality related to polynomials with given Newton polyhedra

Let V⊂Rm be a convex body, symmetric about all coordinate hyperplanes, and let PaV,a≥0, set of algebraic polynomials whose Newton polyhedra are subsets aV. We prove limit equality as a→∞ between the sharp constant in multivariate Markov-Bernstein-Nikolskii type inequalities for from PaV corresponding entire functions exponential with spectrum V.