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

Feng Dai; Andriy Prymak

doi:10.1090/tran/8550

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

Classical Analysis and ODEs 2025-04-15 v3 Numerical Analysis Numerical Analysis

Authors: Feng Dai , Andriy Prymak

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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.

Keywords

bernstein inequality l^p spaces c^2-domains tangential derivatives discretization marcinkiewicz inequality cubature formula

Cite

@article{arxiv.2010.06728,
  title  = {$L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization},
  author = {Feng Dai and Andriy Prymak},
  journal= {arXiv preprint arXiv:2010.06728},
  year   = {2025}
}

Comments

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

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

Abstract

Keywords

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