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<p>Markov-type inequalities provide estimates of the ratio of the norm of derivatives of a polynomial and the norm of the polynomial itself, and so, they play a main role in approximation theory. Weighted Sobolev spaces constitute the framework of the study of Sobolev orthogonal polynomials. In this paper, we prove new Markov-type inequalities in weighted Sobolev spaces on the real line with exponential weights and on the unit circle, respectively, with doubling weights. Also, we improve some previous Markov-type inequalities with generalized Laguerre and Hermite weights.</p>

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Markov-Type Inequalities on Weighted Sobolev Spaces with Doubling Weights

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  • 发表日期：

    2025年7月2日

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  • Francisco Marcellán,
  • José, M. Rodríguez

摘要

Markov-type inequalities provide estimates of the ratio of the norm of derivatives of a polynomial and the norm of the polynomial itself, and so, they play a main role in approximation theory. Weighted Sobolev spaces constitute the framework of the study of Sobolev orthogonal polynomials. In this paper, we prove new Markov-type inequalities in weighted Sobolev spaces on the real line with exponential weights and on the unit circle, respectively, with doubling weights. Also, we improve some previous Markov-type inequalities with generalized Laguerre and Hermite weights.