{"paper":{"title":"The $W^{s,p}$-boundedness of stationary wave operators for the Schr\\\"odinger operator with inverse-square potential","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Jiqiang Zheng, Xiaoyan Su","submitted_at":"2021-10-05T11:58:37Z","abstract_excerpt":"In this paper, we investigate the $W^{s,p}$-boundedness for stationary wave operators of the Schr\\\"odinger operator with inverse-square potential $$\\mathcal L_a=-\\Delta+\\tfrac{a}{|x|^2}, \\quad a\\geq -\\tfrac{(d-2)^2}{4},$$ in dimension $d\\geq 2$. We construct the stationary wave operators in terms of integrals of Bessel functions and spherical harmonics, and prove that they are $W^{s,p}$-bounded for certain $p$ and $s$ which depend on $a$. As corollaries, we solve some open problems associated with the operator $\\mathcal L_a$, which include the dispersive estimates and the local smoothing estim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.01969","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.01969/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}