Journal of Inequalities and Applications
Volume 2005 (2005), Issue 4, Pages 413-421

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

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.


Bernstein inequalities are given for polynomials of degree at most 2m (where mn), 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.