Volume 24, pp. 88-93, 2006.

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey

José M. Rodríguez, Venancio Álvarez, Elena Romera, and Domingo Pestana


In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in Approximation Theory. We also find conditions under which the evaluation operator is bounded.

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Key words

Sobolev spaces, weights, orthogonal polynomials

AMS subject classifications

41A10, 46E35, 46G10

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