English

On Bernstein's inequality for polynomials

Classical Analysis and ODEs 2019-03-27 v1

Abstract

Bernstein's classical inequality asserts that given a trigonometric polynomial TT of degree n1n\geq1, the sup-norm of the derivative of TT does not exceed nn times the sup-norm of TT. We present various approaches to prove this inequality and some of its natural extensions/variants, especially when it comes to replacing the sup-norm with the LpnormL^p-norm.

Keywords

Cite

@article{arxiv.1903.10801,
  title  = {On Bernstein's inequality for polynomials},
  author = {Hervé Queffélec and Rachid Zarouf},
  journal= {arXiv preprint arXiv:1903.10801},
  year   = {2019}
}
R2 v1 2026-06-23T08:19:19.826Z