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A Cohen-Type Inequality for Jacobi-Sobolev Expansions

Journal of Inequalities and Applications20082007:093815

https://doi.org/10.1155/2007/93815

©  Bujar Xh. Fejzullahu 2007

Received: 21 August 2007

Accepted: 11 December 2007

Published: 6 February 2008

Abstract

Let be the Jacobi measure supported on the interval [-1, 1]. Let us introduce the Sobolev-type inner product , where . 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.

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Authors’ Affiliations

(1)
Faculty of Mathematics and Sciences, University of Prishtina

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Copyright

© Bujar Xh. Fejzullahu 2007

This article is published under license to BioMed Central Ltd. 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.