Sharp Lp Bernstein type inequality for cuspidal domains in Rd

Abstract In this paper we verify a sharp Bernstein type inequality for multivariate algebraic polynomials in L p norm on general cuspidal domains which is based on a proper measure of the distance to the boundary of the domain. In particular, in case of Lip γ cuspidal graph domains the exact rate is given by n 2 γ − 1 .