{"paper":{"title":"Boundedness of Monge-Ampere singular integral operators on Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chin-Cheng Lin, Ming-Yi Lee, Yongshen Han","submitted_at":"2017-09-11T07:40:45Z","abstract_excerpt":"Let $\\phi: \\Bbb R^n \\mapsto \\Bbb R$ be a strictly convex and smooth function, and $\\mu= \\text{det}\\,D^2 \\phi$ be the Monge-Amp\\`ere measure generated by $\\phi.$ For $x\\in \\Bbb R^n$ and $t>0$, let $S(x,t):=\\{y\\in \\Bbb R^n: \\phi(y)<\\phi(x)+\\nabla \\phi(x)\\cdot(y-x)+t\\}$ denote the section. If $\\mu$ satisfies the doubling property, Caffarelli and Guti\\'errez (Trans. AMS 348:1075--1092, 1996) provided a variant of the Calder\\'on-Zygmund decomposition and a John-Nirenberg-type inequality associated with sections. Under a stronger uniform continuity condition on $\\mu$, they also (Amer. J. Math. 119:4"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03278","kind":"arxiv","version":2},"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"}