A simple characterization of weighted Sobolev spaces with bounded multiplication operator

• Autores: José Manuel Rodríguez García
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 153, Nº 1, 2008, págs. 53-72
• Idioma: inglés
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• Resumen

  • In this paper we give a simple characterization of weighted Sobolev spaces (with piecewise monotone weights) such that the multiplication operator is bounded: it is bounded if and only if the support of µ0 is large enough. We also prove some basic properties of the appropriate weighted Sobolev spaces. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials.