Approximation by polynomials and smooth functions in Sobolev spaces with respect to measures Original Research Article

The density of polynomials is straightforward to prove in Sobolev spaces Wk,p((a,b)), but there exist only partial results in weighted Sobolev spaces; here we improve some of these theorems. The situation is more complicated in infinite intervals, even for weighted Lp spaces; besides, in the present paper we have proved some other results for weighted Sobolev spaces in infinite intervals.