{"paper":{"title":"Boundedness of Calder\\'on--Zygmund operators on ball Campanato-type function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Dachun Yang, Hongchao Jia, Yiqun Chen","submitted_at":"2022-08-12T13:26:04Z","abstract_excerpt":"Let $X$ be a ball quasi-Banach function space on ${\\mathbb R}^n$ satisfying some mild assumptions. In this article, the authors first find a reasonable version $\\widetilde{T}$ of the Calder\\'on--Zygmund operator $T$ on the ball Campanato-type function space $\\mathcal{L}_{X,q,s,d}(\\mathbb{R}^n)$ with $q\\in[1,\\infty)$, $s\\in\\mathbb{Z}_+^n$, and $d\\in(0,\\infty)$. Then the authors prove that $\\widetilde{T}$ is bounded on $\\mathcal{L}_{X,q,s,d}(\\mathbb{R}^n)$ if and only if, for any $\\gamma\\in\\mathbb{Z}^n_+$ with $|\\gamma|\\leq s$, $T^*(x^{\\gamma})=0$, which is hence sharp. Moreover, $\\widetilde{T}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.06266","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.06266/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}