{"paper":{"title":"Weak And Strong Type Estimates for Maximal Truncations of Calder\\'on-Zygmund Operators on $ A_p$ Weighted Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eric T. Sawyer, Henri Martikainen, Ignacio Uriarte-Tuero, Maria Carmen Reguera, Michael T. Lacey, Tuomas Orponen, Tuomas P. Hyt\\\"onen","submitted_at":"2011-03-27T16:10:52Z","abstract_excerpt":"For 1<p< \\infty, weight w \\in A_p, and any L ^2 -bounded Calder\\'on-Zygmund operator T, we show that there is a constant C(T,P) so that we prove the sharp norm dependence on T_#, the maximal truncations of T, in both weak and strong type L^p(w) norms. Namely, for the weak type norm, T_# maps L^p(w) to weak-L^p(w) with norm at most \\|w\\|_{A_p}. And for the strong type norm, the norm estimate is \\|w\\|_{A_p}^{\\max(1, (p-1) ^{-1})}. These estimates are not improvable in the power of \\lVert w\\rVert_{A_p}. Our argument follows the outlines of the arguments of Lacey-Petermichl-Reguera (Math.\\ Ann.\\ 2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5229","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"}