{"paper":{"title":"Strichartz estimates for the magnetic Schr\\\"odinger equation with potentials $V$ of critical decay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Seonghak Kim, Youngwoo Koh","submitted_at":"2016-02-02T05:06:51Z","abstract_excerpt":"We study the Strichartz estimates for the magnetic Schr\\\"odinger equation in dimension $n\\geq3$. More specifically, for all Schr\\\"odinger admissible pairs $(r,q)$, we establish the estimate\n  $$\n  \\|e^{itH}f\\|_{L^{q}_{t}(\\mathbb{R}; L^{r}_{x}(\\mathbb{R}^n))} \\leq C_{n,r,q,H} \\|f\\|_{L^2(\\mathbb{R}^n)}\n  $$ when the operator $H= -\\Delta_A +V$ satisfies suitable conditions. In the purely electric case $A\\equiv0$, we extend the class of potentials $V$ to the Fefferman-Phong class. In doing so, we apply a weighted estimate for the Schr\\\"odinger equation developed by Ruiz and Vega. Moreover, for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00789","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"}