{"paper":{"title":"The Garnett-Jones Theorem on BMO spaces associated with operators and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Ji Li, Liang Song, Lixin Yan, Peng Chen, Xuan Thinh Duong","submitted_at":"2023-04-17T20:48:31Z","abstract_excerpt":"Let $X$ be a metric space with doubling measure, and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel satisfies the Gaussian upper bound. Let $f$ be in the space $ {\\rm BMO}_L(X)$ associated with the operator $L$ and we define its distance from the subspace $L^{\\infty}(X)$ under the $ {\\rm BMO}_L(X)$ norm as follows: $$\n  {\\rm dist} (f, L^{\\infty}):= \\inf_{g\\in L^{\\infty}} \\|f -g\\|_{{\\rm BMO}_L(X)}. $$ In this paper we prove that ${\\rm dist} (f, L^{\\infty})$ is equivalent to the infimum of the constant $\\varepsilon$ in the John-Nirenberg inequality for the space ${\\rm B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.08606","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/2304.08606/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"}