Markov and Bernstein type inequalities on subsets of \([-1,1]\) and \([- \pi,\pi]\)
type: Item
instance of: scholarly article
title: Markov and Bernstein type inequalities on subsets of \([-1,1]\) and \([- \pi,\pi]\)
zbMATH Open document ID: 0808.42001
DOI: 10.1007/BF01874312
author: Peter Borwein
author: Tamás Erdélyi
published in: Acta Mathematica Hungarica
publication date: 1995-03-12T00:00:00Z
review text: The authors prove two theorems extending Markov's and Bernstein's inequalities to arbitrary subsets of \([-1,1]\) and \([-\pi,\pi]\), respectively. One of the theorems reads as follows: Let \(0< a\leq 2\pi\), \(0< L\leq 1\), let \(A\) be a closed subset of \([0,2\pi]\) with Lebesgue measure \(m(A)\geq 2\pi- a\). There is an absolute constant \(c> 0\) such that \[ \max_{t\in I} | p'(t)|\leq cL^{-1} (n+ n^ 2 a)\max_{t\in A} | p(t)| \] for every real trigonometric polynomial \(p\) of degree at most \(n\), and for every subinterval \(I\) of \(A\) with length at least \(La\).
reviewed by: László Leindler
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 638248
zbMATH Keywords: Markov inequality
zbMATH Keywords: Bernstein inequality
zbMATH Keywords: real trigonometric polynomial
MaRDI profile type: Publication
cites work: Markov type estimates for derivatives of polynomials of special type
cites work: Remez-Type Inequalities on the Size of Generalized Polynomials
cites work: Q5534403
description: scientific article; zbMATH DE number 638248