{"paper":{"title":"Fractional maximal operators with weighted Hausdorff content","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hiroki Saito, Hitoshi Tanaka, Toshikazu Watanabe","submitted_at":"2017-10-23T01:56:47Z","abstract_excerpt":"Let $n\\ge 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator ${\\mathfrak M}{\\alpha}$ of order $\\alpha$, $0\\le\\alpha<n$, on the weighted Choquet-Lorentz space $L^{p,q}(H_{w}^{d})$, where the weight $w$ is arbitrary and the underlying measure is the weighted $d$-dimensional Hausdorff content $H^{d}_{w}$, $0<d\\le n$. Concerning a dependence of two parameters $\\alpha$ and $d$, we establish a general form of the Fefferman-Stein type inequalities for ${\\mathfrak M}_{\\alpha}$. Our results contain the works of Adams, \\cite{Ad}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08061","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"}