{"paper":{"title":"Boundedness of Maximal Calder\\'on-Zygmund Operators on Non-homogeneous Metric Measure Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Suile Liu, Yan Meng","submitted_at":"2013-08-27T08:38:23Z","abstract_excerpt":"Let $(\\cx,\\,d,\\,\\mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors show that for the maximal Calder\\'on-Zygmund operator associated with a singular integral whose kernel satisfies the standard size condition and the H\\\"ormander condition, its $L^p(\\mu)$ boundedness with $p\\in(1,\\infty)$ is equivalent to its boundedness from $L^1(\\mu)$ into $L^{1,\\infty}(\\mu)$. Moreover, applying this, together with a new Cotlar type inequality, the authors show that if the Calder\\'on-Zygmund operator $T$ is bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5796","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"}