{"paper":{"title":"A reverse Riesz estimate combined with a spectral gap implies a Poincar\\'e inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.OA"],"primary_cat":"math.FA","authors_text":"C\\'edric Arhancet","submitted_at":"2026-07-09T10:07:41Z","abstract_excerpt":"Working at the level of an Abel-ergodic sectorial operator $A$ on a Banach space $X$ and an unbounded operator $\\partial$ defined on a subspace $X$ in another Banach space $Y$, we show that a single reverse Riesz estimate $\\|A^\\alpha x\\|_X \\lesssim \\|\\partial x\\|_Y$ for some $0 < \\alpha < 1$, combined with the condition $0 \\in \\rho(A_0)$, where $A_0$ is the part of $A$ on the closure of the range of $A$, implies the Poincar\\'e inequality $\\|x - P(x)\\|_X \\lesssim \\|\\partial x\\|_Y$, where $P$ is the Abel-ergodic projection onto the kernel of $A$. The condition $0 \\in \\rho(A_0)$ is the natural ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08322","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/2607.08322/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"}