[{"external_id":{"arxiv":["1503.02716"]},"day":"01","OA_type":"green","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1503.02716"}],"page":"1273-1298","date_updated":"2026-06-25T07:36:26Z","publisher":"Springer Nature","author":[{"last_name":"Killip","full_name":"Killip, R.","first_name":"R."},{"full_name":"Miao, C.","last_name":"Miao","first_name":"C."},{"last_name":"Visan","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica"},{"first_name":"J.","last_name":"Zhang","full_name":"Zhang, J."},{"first_name":"J.","last_name":"Zheng","full_name":"Zheng, J."}],"_id":"22042","oa":1,"quality_controlled":"1","publication_status":"published","arxiv":1,"publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"title":"Sobolev spaces adapted to the Schrödinger operator with inverse-square potential","mathsc":["35P25","35Q55"],"year":"2018","intvolume":"       288","issue":"3-4","type":"journal_article","scopus_import":"1","date_published":"2018-04-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"Mathematische Zeitschrift","doi":"10.1007/s00209-017-1934-8","OA_place":"repository","extern":"1","citation":{"short":"R. Killip, C. Miao, M. Vişan, J. Zhang, J. Zheng, Mathematische Zeitschrift 288 (2018) 1273–1298.","ama":"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>","ieee":"R. Killip, C. Miao, M. Vişan, J. Zhang, and J. Zheng, “Sobolev spaces adapted to the Schrödinger operator with inverse-square potential,” <i>Mathematische Zeitschrift</i>, vol. 288, no. 3–4. Springer Nature, pp. 1273–1298, 2018.","ista":"Killip R, Miao C, Vişan M, Zhang J, Zheng J. 2018. Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. Mathematische Zeitschrift. 288(3–4), 1273–1298.","chicago":"Killip, R., C. Miao, Monica Vişan, J. Zhang, and J. Zheng. “Sobolev Spaces Adapted to the Schrödinger Operator with Inverse-Square Potential.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00209-017-1934-8\">https://doi.org/10.1007/s00209-017-1934-8</a>.","mla":"Killip, R., et al. “Sobolev Spaces Adapted to the Schrödinger Operator with Inverse-Square Potential.” <i>Mathematische Zeitschrift</i>, vol. 288, no. 3–4, Springer Nature, 2018, pp. 1273–98, doi:<a href=\"https://doi.org/10.1007/s00209-017-1934-8\">10.1007/s00209-017-1934-8</a>.","apa":"Killip, R., Miao, C., Vişan, M., Zhang, J., &#38; Zheng, J. (2018). Sobolev spaces adapted to the Schrödinger operator with inverse-square potential. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-017-1934-8\">https://doi.org/10.1007/s00209-017-1934-8</a>"},"oa_version":"Preprint","article_type":"original","date_created":"2026-06-19T07:46:14Z","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We study the L p-theory for the Schrödinger operatorLa with inverse-square potential\r\na|x|^−2. Our main result describes when L p-based Sobolev spaces defined in terms of the\r\noperator (La)^s/2 agree with those defined via (−\u0002)^s/2.We consider all regularities 0 < s < 2.\r\nIn order to make the paper self-contained, we also review (with proofs) multiplier theorems,\r\nLittlewood–Paley theory, and Hardy-type inequalities associated to the operator La."}],"volume":288,"month":"04","status":"public"}]