Sobolev Spaces on Quasi-K?hler Complex Varieties

If V is an irreducible quasi-K?hler complex variety and E is a vector bundle over reg(V), the author proves that W_(0)~(1,2)(reg(V), E) = W~(1,2)(reg(V), E), and that for dimcreg(V) 1, the natural inclusion W~(1,2)■(reg(V), E)L~2(reg(V), E) is compact, the natural inclusion W~(1,2)(reg(V), E)■ (reg(V), E) is continuous.