$L_p$ Markov exponent of certain UPC sets

TL;DR

This paper establishes precise $L_p$ Markov inequalities for derivatives of multivariate polynomials over a broad class of UPC domains, advancing understanding of polynomial approximation in these regions.

Contribution

It introduces sharp $L_p$ Markov inequalities for multivariate polynomials on UPC domains, a significant extension of existing polynomial approximation theory.

Findings

Derived sharp $L_p$ Markov inequalities for multivariate polynomials.

Extended polynomial approximation results to a wide family of UPC domains.

Provided new bounds that improve upon previous inequalities.

Abstract

In this paper we give sharp $L_p$ Markov type inequalities for derivatives of multivariate polynomials for a wide family of UPC domains.