{"paper":{"title":"Weighted estimates for powers and Smoothing estimates of Schr\\\"odinger operators with inverse-square potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fu Ken Ly, Ji Li, Piero D'Ancona, The Anh Bui, Xuan Thinh Duong","submitted_at":"2016-09-07T11:08:11Z","abstract_excerpt":"Let $\\mathcal{L}_a$ be a Schr\\\"odinger operator with inverse square potential $a|x|^{-2}$ on $\\mathbb{R}^d, d\\geq 3$. The main aim of this paper is to prove weighted estimates for fractional powers of $\\mathcal{L}_a$. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to $\\mathcal{L}_a$. As an application, we obtain smoothing estimates regarding the propagator $e^{it\\mathcal{L}_a}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01938","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":""},"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"}