Interpolating and orthogonal polynomials on fractals (Q909922)

A set \(F\subset {\mathbb{R}}^ n\) is said to preserve Markov's inequality if for every \(k\in {\mathbb{N}}\) there is a constant c(n,k,F) such that, for all polynomials P of degree \(\leq k\) and all balls \(B(x_ 0,r)\) with \(x_ 0\in F\) and \(0<r\leq 1\), we have \(\max_{F\cap B}| \nabla P| \leq c/r\max_{F\cap B}| P|.\) Examples of such sets are the Cantor set, the Koch snowflake and the closure of a domain with locally Lipschitzian boundary. The author studies interpolation to smooth functions on F with the points of interpolation belong to F.