This article is cited in 5 papers

A Sharp Markov Brothers-Type Inequality in the Spaces $L_\infty$ and $L_1$ on the Segment

I. E. Simonov

Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg

Abstract: The inequality between the uniform norm of the derivative of order $\ell$ of an algebraic polynomial of degree $n$ and the $L_1$-norm of the polynomial itself on a segment are studied. For all $\ell\ge(n-1)/3$, the exact constant and the extremal polynomial are written out.

Keywords: Markov brothers' inequality, algebraic polynomial, trigonometric polynomial, Chebyshev polynomial, Legendre polynomial.

UDC: 517.518.862

Received: 18.04.2012

DOI: 10.4213/mzm10171

 English version: Mathematical Notes, 2013, 93:4, 607–615

Bibliographic databases:

• 
• 
• 
• 
• 
•