{"paper":{"title":"Sobolev spaces adapted to the Schr\\\"odinger operator with inverse-square potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Miao, J. Zhang, J. Zheng, M. Visan, R. Killip","submitted_at":"2015-03-09T22:35:05Z","abstract_excerpt":"We study the $L^p$-theory for the Schr\\\"odinger operator $\\mathcal L_a$ with inverse-square potential $a|x|^{-2}$. Our main result describes when $L^p$-based Sobolev spaces defined in terms of the operator $(\\mathcal L_a)^{s/2}$ agree with those defined via $(-\\Delta)^{s/2}$. We consider all regularities $0<s<2$.\n  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 $\\mathcal L_a$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02716","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}