{"paper":{"title":"Weak type $(1, 1)$ of Riesz transform on some direct product manifolds with exponential volume growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hong-Quan Li, Jie-Xiang Zhu","submitted_at":"2023-04-10T00:24:36Z","abstract_excerpt":"In this paper we are concerned with the Riesz transform on the direct product manifold ${\\mathbb{H}}^n \\times M$, where ${\\mathbb{H}}^n$ is the $n$-dimensional real hyperbolic space and $M$ is a connected complete non-compact Riemannian manifold satisfying the volume doubling property and generalized Gaussian or sub-Gaussian upper estimates for the heat kernel. We establish its weak type $(1,1)$ property. In addition, we obtain the weak type $(1, 1)$ of the heat maximal operator in the same setting. Our arguments also work for a large class of direct product manifolds with exponential volume g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.04335","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/2304.04335/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"}