{"paper":{"title":"Weighted $L^p$ Estimates of Kato Square Roots Associated to Degenerate Elliptic Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Junqiang Zhang","submitted_at":"2015-09-18T00:19:58Z","abstract_excerpt":"Let $w$ be a Muckenhoupt $A_2(\\mathbb{R}^n)$ weight and $L_w:=-w^{-1}\\mathop\\mathrm{div}(A\\nabla)$ the degenerate elliptic operator on the Euclidean space $\\mathbb{R}^n$, $n\\geq 2$. In this article, the authors establish some weighted $L^p$ estimates of Kato square roots associated to the degenerate elliptic operators $L_w$. More precisely, the authors prove that, for $w\\in A_{p}(\\mathbb{R}^n)$, $p\\in(\\frac{2n}{n+1},\\,2]$ and any $f\\in C^\\infty_c(\\mathbb{R}^n)$, $\\|L_w^{1/2}(f)\\|_{L^p(w,\\,\\mathbb{R}^n)}\\sim \\|\\nabla f\\|_{L^p(w,\\,\\mathbb{R}^n)}$, where $C_c^\\infty(\\mathbb{R}^n)$ denotes the set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05478","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"}