Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 93815, 10 pages
A Cohen-Type Inequality for Jacobi-Sobolev Expansions
Faculty of Mathematics and Sciences, University of Prishtina, Mother Teresa 5, Prishtina 10000, Kosovo, Serbia
Received 21 August 2007; Revised 20 November 2007; Accepted 11 December 2007
Academic Editor: Wing-Sum Cheung
Copyright © 2007 Bujar Xh. Fejzullahu. 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.
Let be the
Jacobi measure supported on the interval [-1, 1]. Let us
introduce the Sobolev-type inner product
In this paper we prove a Cohen-type inequality for the Fourier
expansion in terms of the orthonormal polynomials associated with
the above Sobolev inner product. We follow Dreseler and Soardi
(1982) and Markett (1983) papers, where such inequalities were
proved for classical orthogonal expansions.