Sobolev spaces adapted to the Schrodinger operator with inverse-square potential

We study the -theory for the Schrodinger operator with inverse-square potential . Our main result describes when -based Sobolev spaces defined in terms of the operator agree with those defined via . We consider all regularities . In order to make the paper self-contained, we also review (with proofs) multiplier theorems, Littlewood-Paley theory, and Hardy-type inequalities associated to the operator L-a.