{"paper":{"title":"Linear bounds for Calder\\'{o}n-Zygmund operators with even kernel on UMD spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrei Stoica, Sandra Pott","submitted_at":"2013-10-29T16:32:50Z","abstract_excerpt":"It is well-known that several classical results about Calder\\'{o}n-Zygmund singular integral operators can be extended to \\(X\\)-valued functions if and only if the Banach space \\(X\\) has the UMD property. The dependence of the norm of an \\(X\\)-valued Calder\\'{o}n-Zygmund operator on the UMD constant of the space \\(X\\) is conjectured to be linear. We prove that this is indeed the case for sufficiently smooth Calder\\'{o}n-Zygmund operators with cancellation, associated to an even kernel. Our method uses the Bellman function technique to obtain the right estimates for the norm of dyadic Haar shif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7864","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"}