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A Cohen-Type Inequality for Jacobi-Sobolev Expansions

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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Correspondence to Bujar Xh Fejzullahu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fejzullahu, B.X. A Cohen-Type Inequality for Jacobi-Sobolev Expansions. J Inequal Appl 2007, 093815 (2008). https://doi.org/10.1155/2007/93815

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

Keywords

  • Fourier Expansion
  • Orthogonal Expansion
  • Orthonormal Polynomial
  • Jacobi Measure