Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 93815, 10 pages
Research Article

A Cohen-Type Inequality for Jacobi-Sobolev Expansions

Bujar Xh. Fejzullahu

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 μ be the Jacobi measure supported on the interval [-1, 1]. Let us introduce the Sobolev-type inner product f,g=11f(x)g(x)dμ(x)+Mf(1)g(1)+Nf'(1)g'(1), where M,N0. 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.