On the Order of the Lebesgue Constants for Interpolation by Algebraic Polynomials from Values at Uniform Nodes of a Simplex

For interpolation processes by algebraic polynomials of degree $n$ from values at uniform nodes of an $m$-simplex, where $m\ge2$, we obtain the order of growth in $n$ of the Lebesgue constants, which coincides with that in the one-dimensional case for which Turetskii obtained an asymptotics earlier.