{"paper":{"title":"A T(P) theorem for Sobolev spaces on domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Mart\\'i Prats, Xavier Tolsa","submitted_at":"2014-06-18T15:35:59Z","abstract_excerpt":"Recently, V. Cruz, J. Mateu and J. Orobitg have proved a T(1) theorem for the Beurling transform in the complex plane. It asserts that given $0<s\\leq1$, $1<p<\\infty$ with $sp>2$ and a Lipschitz domain $\\Omega\\subset \\mathbb{C}$, the Beurling transform $Bf=- {\\rm p.v.}\\frac1{\\pi z^2}*f$ is bounded in the Sobolev space $W^{s,p}(\\Omega)$ if and only if $B\\chi_\\Omega\\in W^{s,p}(\\Omega)$.\n  In this paper we obtain a generalized version of the former result valid for any $s\\in \\mathbb{N}$ and for a larger family of Calder\\'on-Zygmund operators in any ambient space $\\mathbb{R}^d$ as long as $p>d$. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4769","kind":"arxiv","version":3},"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"}