Geodesic
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey
Electronic transactions on numerical analysis, Tome 24 (2006), pp. 88-93.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 41A10, 46E35, 46G10
Keywords: Sobolev spaces, weights, orthogonal polynomials 
@article{ETNA_2006__24__a3,
     author = {Rodr{\'\i}guez, Jos\'e M. and \'Alvarez, Venancio and Romera, Elena and Pestana, Domingo},
     title = {Generalized weighted {Sobolev} spaces and applications to {Sobolev} orthogonal polynomials: a survey},
     journal = {Electronic transactions on numerical analysis},
     pages = {88--93},
     publisher = {mathdoc},
     volume = {24},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__24__a3/}
}
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%J Electronic transactions on numerical analysis
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Rodríguez, José M.; Álvarez, Venancio; Romera, Elena; Pestana, Domingo. Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey. Electronic transactions on numerical analysis, Tome 24 (2006), pp. 88-93. http://geodesic.mathdoc.fr/item/ETNA_2006__24__a3/