Best constants in global smoothness preservation inequalities for some multivariate operators (Q1288271)

Using a probabilistic representation of positive operators going back to the classical paper of S. Bernstein the authors give sharp estimates for the modulus of continuity of \(L_tf\). Here \(\{L_t\xi_{t\in T}\) is an approximating family of positive operators acting in the space \(\{f:I^k\to\mathbb{R}\); \(\sup_{x,y}| f(x)-f(y)|<\infty\}\) where \(I^k\) is either \(k\)-simplex or \(\mathbb{R}^k_+\).