$L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization

Abstract

We prove a new Bernstein type inequality in $L^p$ spaces associated with the tangential derivatives on the boundary of a general compact $C^2$-domain. We give two applications: Marcinkiewicz type inequality for discretization of $L^p$ norm and positive cubature formula. Both results are optimal in the sense that the number of function samples used has the order of the dimension of the corresponding space of algebraic polynomials.

the material in this article is based heavily on a part of arXiv:1910.11719

Cited by in corpus (2)

• On Bernstein- and Marcinkiewicz-type inequalities on multivariate $C^{\alpha }$-domains
• Polynomial approximation on $C^2$-domains