ABSTRACT
For multivariate Bernstein-type operators, we consider preservation of the usual l p -modulus of continuity, as well as preservation of classes of functions determined by moduli of continuity. Using a probabilistic approach based on representations in terms of stochastic processes, we establish general bounds and formulae for the involved best constants. Special attention is paid to tensor product operators and to simplicial operators. Some applications and illustrations of the general results to particular operators are also given.
