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

Theodore Kilgore

 Department of Mathematics and Statistics, Auburn University, Auburn 36849, AL, USA
Received 17 September 2003

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.