Álvarez, VenancioPestana, DomingoRodríguez, José M.Romera, Elena2010-01-192010-01-192001Margarita mathematica en memoria de José Javier (Chicho) Guadalupe Hernández (Luis Español y Juan L. Varona, eds), pp. 487-50384-95301-56-3https://hdl.handle.net/10016/649017 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.application/pdfengWeighted Sobolev spacesPolynomial approximationMultiplication operatorSzegö theoremZeroes of orthogonal polynomialsconference paperMatemáticasopen access