GENERALIZED WEIGHTED SOBOLEV SPACES AND APPLICATIONS TO SOBOLEV ORTHOGONAL POLYNOMIALS Ⅱ

We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk+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（?）∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.