Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 93815, 10 pages
doi:10.1155/2007/93815
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

Recommended by Wing-Sum Cheung

Abstract

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,N≥0. 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.