Sobolev spaces adapted to the Schrödinger operator with inverse-square potential Killip, R. Miao, C. Visan, Monica Zhang, J. Zheng, J. 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. Springer Nature 2018 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22042 Killip R, Miao C, Vişan M, Zhang J, Zheng J. Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. <i>Mathematische Zeitschrift</i>. 2018;288(3-4):1273-1298. doi:<a href="https://doi.org/10.1007/s00209-017-1934-8">10.1007/s00209-017-1934-8</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00209-017-1934-8 info:eu-repo/semantics/altIdentifier/issn/0025-5874 info:eu-repo/semantics/altIdentifier/e-issn/1432-1823 info:eu-repo/semantics/altIdentifier/arxiv/1503.02716 info:eu-repo/semantics/openAccess