{"paper":{"title":"Reverse Riesz Inequality on Manifolds with Ends","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dangyang He","submitted_at":"2024-11-26T04:52:16Z","abstract_excerpt":"In our investigation, we focus on the reverse Riesz transform within the framework of manifolds with ends. Such manifolds can be described as the connected sum of finite number of Cartesian products $\\mathbb{R}^{n_i} \\times \\mathcal{M}_i$, where $\\mathcal{M}_i$ are compact manifolds. We rigorously establish the boundedness of this transform across all $L^p$ spaces for $1<p<\\infty$. Notably, existing knowledge indicates that the Riesz transform in such a context demonstrates boundedness solely within a specific range of $L^p$ spaces, typically observed for $1<p<n_*$, where $n_*$ signifies the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17107","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/2411.17107/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"}