Rodríguez, José M.Romera, ElenaPestana, DomingoÁlvarez, Venancio2010-01-192010-01-192002-06Approximation Theory and its Applications, 2002, vol. 18, n. 2, p. 1-321000-9221 (Print)1573-8175 (Online)https://hdl.handle.net/10016/648332 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.-- Part I of this paper published in: Acta Appl. Math. 80(3): 273-308 (2004), available at: http://e-archivo.uc3m.es/handle/10016/6482MR#: MR1928169 (2003h:42034)Zbl#: Zbl 1095.42014^aWe present a definition of general Sobolev spaces with respect to arbitrary measures, $W^{k,p}(\Omega,\mu)$ for $1\leq p\leq\infty$. In Part I [Acta Appl. Math. 80(3): 273-308 (2004), http://e-archivo.uc3m.es/handle/10016/6482] we proved that these spaces are complete under very mild conditions. Now we prove that if we consider certain general types of measures, then $C^\infty_c({\bf R})$ is dense in these spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.application/pdfeng© SpringerSobolev spaces with respect to measuresWeightsOrthogonal polynomialsCompletenessresearch articleMatemáticas10.1007/BF02837397open access