Open Access

Markov and Bernstein inequalities in https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq1_HTML.gif for some weighted algebraic and trigonometric polynomials

Journal of Inequalities and Applications20052005:350524

DOI: 10.1155/JIA.2005.413

Received: 17 September 2003

Published: 31 August 2005

Abstract

Bernstein inequalities are given for polynomials of degree at most https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq2_HTML.gif (where https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq3_HTML.gif ), weighted by https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq4_HTML.gif , in https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq5_HTML.gif norms on https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq6_HTML.gif , and also in related spaces of weighted trigonometric polynomials. Also, Bernstein and Markov inequalities valid on https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq7_HTML.gif are derived for polynomials of degree https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq8_HTML.gif weighted by https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.413/MediaObjects/13660_2003_Article_1525_IEq9_HTML.gif .

Authors’ Affiliations

(1)
Department of Mathematics and Statistics, Auburn University

Copyright

© Kilgore. 2005