{"paper":{"title":"$L^p$-boundedness of wave operators for bi-Schr\\\"odinger operators on the line","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.AP","authors_text":"Haruya Mizutani, Xiaohua Yao, Zijun Wan","submitted_at":"2022-01-13T01:16:16Z","abstract_excerpt":"This paper is devoted to establishing several types of $L^p$-boundedness of wave operators $W_\\pm=W_\\pm(H, \\Delta^2)$ associated with the bi-Schr\\\"odinger operators $H=\\Delta^{2}+V(x)$ on the line $\\mathbb{R}$. Given suitable decay potentials $V$, we firstly prove that the wave and dual wave operators are bounded on $L^p(\\mathbb{R})$ for all $1<p<\\infty$: $$ \\|W_\\pm f\\|_{L^p(\\mathbb{R})}+\\|W_\\pm^* f\\|_{L^p(\\mathbb{R})}\\lesssim \\|f\\|_{L^p(\\mathbb{R})},$$ which are further extended to the $L^p$-boundedness on the weighted spaces $L^p(\\mathbb{R},w)$ with general even $A_p$-weights $w$ and to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.04758","kind":"arxiv","version":3},"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/2201.04758/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"}