Markov-type Inequalities for Surface Gradients of Multivariate Polynomials Original Research Article

Let K⊂Rd be a compact set with a smooth boundary and consider a polynomial p of total degree ⩽n such that ∥p∥C(K)⩽1. Then we show that ∣DTp(x)∣=o(n2) for any x ∈ Bd K and T a tangential direction at x. Moreover, the o(n2) term is given in terms of the modulus of smoothness of Bd K.