Journal of Inequalities and Applications
Volume 2 (1998), Issue 3, Pages 285-296
doi:10.1155/S1025583498000186
Two polynomial division inequalities in Lp
Université de Paris-Sud, Mathématiques Bât. 425, Orsay Cedex 91405, France
Received 4 March 1997; Revised 6 August 1997
Copyright © 1998 P. Goetgheluck. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper is a first attempt to give numerical values for constants Cp and C′p, in classical estimates ‖P‖≤Cpn‖xP‖ and ‖P‖≤C′pn2‖(1−x)P‖ where P is an algebraic polynomial of degree at most n (n>0) and ‖⋅‖ denotes the p-metric on [−1,1]. The basic tools are Markov and Bernstein inequalities.