{"paper":{"title":"Nonexistence of Bounded Linear Extension Operators for Limiting Besov Traces on Metric Measure Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aleksei Y. Chikalov","submitted_at":"2026-07-13T14:28:50Z","abstract_excerpt":"Let $p\\in[1,\\infty)$, and let $X=(X,d,\\mu)$ be a metric measure space such that $\\mu$ is uniformly locally doubling and $X$ supports a local weak $(1,p)$-Poincar\\'e inequality. Given $\\theta\\in(0,p)$ and an Ahlfors--David codimension-$\\theta$ regular set $E\\subset X$, the trace-space of the Besov space $B^{\\theta/p}_{p,1}(X)$ to $E$ can be identified with $L_p(E,\\mathcal{H}_{\\theta}\\lfloor_E)$. If there exists a measurable set $A\\subset E$ with $0<\\mathcal H_\\theta(A)<\\infty$ such that $\\mathcal H_\\theta\\lfloor_A$ is nonatomic, we prove that there is no bounded linear extension operator $\\oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11604","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/2607.11604/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"}