{"paper":{"title":"New estimates for the Beurling-Ahlfors operator on differential forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Leonid Slavin, Stefanie Petermichl","submitted_at":"2009-01-04T00:01:43Z","abstract_excerpt":"We establish new $p$-estimates for the norm of the generalized Beurling--Ahlfors transform $\\mathcal{S}$ acting on form-valued functions. Namely, we prove that $\\norm{\\mathcal{S}}_{L^p(\\R^n;\\Lambda)\\to L^p(\\R^n;\\Lambda)}\\leq n(p^{*}-1)$ where $p^*=\\max\\{p, p/(p-1)\\},$ thus extending the recent Nazarov--Volberg estimates to higher dimensions. The even-dimensional case has important implications for quasiconformal mappings. Some promising prospects for further improvement are discussed at the end."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0345","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"}