{"paper":{"title":"Boundedness of Calder\\'on-Zygmund Operators on Non-homogeneous Metric Measure Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dachun Yang, Dongyong Yang, Suile Liu, Tuomas Hyt\\\"onen","submitted_at":"2010-11-12T15:05:50Z","abstract_excerpt":"Let $({\\mathcal X}, d, \\mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\\mu(\\{x\\})=0$ for all $x\\in{\\mathcal X}$. In this paper, we show that the boundedness of a Calder\\'on-Zygmund operator $T$ on $L^2(\\mu)$ is equivalent to that of $T$ on $L^p(\\mu)$ for some $p\\in (1, \\infty)$, and that of $T$ from $L^1(\\mu)$ to $L^{1,\\,\\infty}(\\mu).$ As an application, we prove that if $T$ is a Calder\\'on-Zygmund operator bounded on $L^2(\\mu)$, then its maximal operator is bounded on $L^p(\\mu)$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2937","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"}