Journal of Inequalities and Applications
Volume 2005 (2005), Issue 4, Pages 413-421
doi:10.1155/JIA.2005.413
Markov and Bernstein inequalities in LP for some weighted algebraic and trigonometric polynomials
Department of Mathematics and Statistics, Auburn University, Auburn 36849, AL, USA
Received 17 September 2003
Copyright © 2005 Theodore Kilgore. 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
Bernstein inequalities are given for polynomials of degree at most
2m (where m≤n), weighted by (1+x2)−n, in Lp norms on (−∞,∞), and also in related spaces of weighted
trigonometric polynomials. Also, Bernstein and Markov inequalities
valid on [0,∞) are derived for polynomials of degree m weighted by (1+t)−n.