{"paper":{"title":"$L^p$ Boundedness of Commutators of Riesz Transforms associated to Schr\\\"{o}dinger Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lizhong Peng, Pengtao Li, Zihua Guo","submitted_at":"2008-02-21T15:10:44Z","abstract_excerpt":"In this paper we consider $L^p$ boundedness of some commutators of Riesz transforms associated to Schr\\\"{o}dinger operator $P=-\\Delta+V(x)$ on $\\mathbb{R}^n, n\\geq 3$. We assume that $V(x)$ is non-zero, nonnegative, and belongs to $B_q$ for some $q \\geq n/2$. Let $T_1=(-\\Delta+V)^{-1}V,\\ T_2=(-\\Delta+V)^{-1/2}V^{1/2}$ and $T_3=(-\\Delta+V)^{-1/2}\\nabla$. We obtain that $[b,T_j] (j=1,2,3)$ are bounded operators on $L^p(\\mathbb{R}^n)$ when $p$ ranges in a interval, where $b \\in \\mathbf{BMO}(\\mathbb{R}^n)$. Note that the kernel of $T_j (j=1,2,3)$ has no smoothness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3128","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"}