Weierstrass' Theorem in Weighted Sobolev Spaces

where ∆ := ∪j=0supp wj . It is obvious that W 0,∞(∆, w) = L∞(∆, w). Weighted Sobolev spaces are an interesting topic in many fields of Mathematics (see e.g. [HKM], [K], [Ku], [KO], [KS] and [T]). In [ELW1], [EL] and [ELW2] the authors study some examples of Sobolev spaces for p = 2 with respect to general measures instead of weights, in relation with ordinary differential equations and Sobolev orthogonal polynomials. The papers [RARP1], [RARP2], [R1] and [R2] are the beginning of a theory of Sobolev spaces with respect to general measures for 1 ≤ p ≤ ∞. This theory plays an important role in the location of the zeroes of the Sobolev orthogonal polynomials (see [LP], [RARP2] and [R1]). The location of these zeroes allows to prove results on the asymptotic behaviour of Sobolev orthogonal polynomials (see [LP]).