A Cohen-Type Inequality for Jacobi-Sobolev Expansions. (6th February 2008)

• Record Type: Journal Article
• Authors: Fejzullahu, Bujar Xh.
• Other Names: Cheung Wing-Sum Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2007(2007)
• Publication Date: 2008-02-06
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2007/93815
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : Letμ be the Jacobi measure supported on the interval [-1, 1]. Let us introduce the Sobolev-type inner product〈 f, g 〉 = ∫ − 1 1 f ( x ) g ( x ) d μ ( x ) + M f ( 1 ) g ( 1 ) + N f ' ( 1 ) g ' ( 1 ), whereM, 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.