On Weighted Sobolev Spaces

We study density and extension problems for weighted Sobolev spaces on bounded (e, 8) domains (D when a doubling weight w satisfies the weighted Poincare inequality on cubes near the boundary of (D and when it is in the Muckenhoupt Ap class locally in D. Moreover, when the weights W/(JC) are of the form dist(*, M/)', a, G IR, Mi C (D that are doubling, we are able to obtain some extension theorems on (e, oo) domains.