  We study Hochschild homology and cohomology for some polynomial algebras
mixing both ``classical'' relations ($XY-YX=1$) and ``quantum'' relations
($XY={\l}YX$). More specifically, we prove that the algebra of differential
operators on any quantum affine space (quantum Weyl algebra) have the same
Hochschild homology, and satisfy the same duality relation, as the classical
Weyl algebra does.
