Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials II

We present a definition of general Sobolev spaces with respect to arbitrary measures, W^{k, p} (Ω, μ) for 1 ≤p≤∞. In RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then C ₆ ^∞ (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. Research Partially Supported by a Grant from DGES (MEC), Spain.