{"paper":{"title":"Maximal inequalities and Riesz transforms for vector-valued magnetic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelaziz Rhandi, Davide Addona, Luca Lorenzi. El Maati Ouhabaz, Vincenzo Leone","submitted_at":"2026-05-19T06:48:37Z","abstract_excerpt":"We consider vector-valued magnetic Schr\\\"odinger operators $-\\bm \\Delta_{\\bm a}+V$ with magnetic potential $\\bm a \\in L^2_{\\mathrm{loc}}(\\mathbb{R}^d;\\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries belong to $L^1_{\\mathrm{loc}}(\\mathbb{R}^d)$. We prove maximal inequalities in $L^p(\\mathbb{R}^d;\\mathbb{C}^m)$, $p\\in[1,\\infty)$ and the boundedness of the Riesz transforms $(\\nabla - i\\bm a)(-\\bm \\Delta_{\\bm a}+V)^{-\\frac{1}{2}}$ and $V^{\\alpha}(-\\bm \\Delta_{\\bm a}+V)^{-\\alpha}$ on $L^p(\\mathbb{R}^d;\\mathbb{C}^m)$ for every $p \\in (1,2]$ and every $\\alpha\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19438","kind":"arxiv","version":1},"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/2605.19438/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"}