{"paper":{"title":"Carleman estimates and boundedness of associated multiplier operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Eunhee Jeong, Sanghyuk Lee, Yehyun Kwon","submitted_at":"2018-03-08T11:08:33Z","abstract_excerpt":"Let $P(D)$ be the Laplacian $\\Delta,$ or the wave operator $\\square$. The following type of Carleman estimate is known to be true on a certain range of $p,q$: \\[ \\|e^{v\\cdot x}u\\|_{L^q(\\mathbb{R}^d)} \\le C\\|e^{v\\cdot x}P(D)u\\|_{L^p(\\mathbb{R}^d)} \\] with $C$ independent of $v\\in \\mathbb{R}^d$. The estimates are consequences of the uniform Sobolev type estimates for second order differential operators due to Kenig-Ruiz-Sogge \\cite{KRS} and Jeong-Kwon-Lee \\cite{JKL}. The range of $p,q$ for which the uniform Sobolev type estimates hold was completely characterized for the second order differentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03040","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":""},"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"}