Sobolev spaces adapted to the Schrödinger operator with inverse-square potential We study the L p-theory for the Schrödinger operatorLa with inverse-square potential a|x|^−2. Our main result describes when L p-based Sobolev spaces defined in terms of the operator (La)^s/2 agree with those defined via (−)^s/2.We consider all regularities 0 < s < 2. 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 La. 288 3-4 1273-1298 1273-1298 Springer Nature