{"paper":{"title":"The $L^p$-continuity of wave operators for fractional order Schr\\\"odinger operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Burak Erdogan, Michael Goldberg, William Green","submitted_at":"2025-09-22T16:41:13Z","abstract_excerpt":"We consider fractional Schr\\\"odinger operators $H=(-\\Delta)^\\alpha+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2\\alpha$, $\\alpha>1$. We show that the wave operators extend to bounded operators on $L^p(\\mathbb R^n)$ for all $1\\leq p\\leq\\infty$ under conditions on the potential that depend on $n$ and $\\alpha$ analogously to the case when $\\alpha\\in \\mathbb N$. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schr\\\"odinger operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.18003","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/2509.18003/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"}