Inverse theorems for multidimensional Bernstein operators (Q1068304)

Let \(B_ f\) be the m-dimensional Bernstein polynomials on a simplex or on a cube. The class of functions for which \(\| B_ nf-f\| =O(n^{- \alpha})\) is determined. That is, necessary and sufficient conditions on the smoothness of f in the simplex or the cube and especially near their boundaries are given so that \(\| B_ nf-f\| =O(n^{-\alpha})\). Interpolation of spaces, and in particular the characterization of the interpolation space, is one of the tools used.