{"paper":{"title":"Vanishing Mean Oscillation Spaces Associated with Operators Satisfying Davies-Gaffney Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Wen Yuan, Yiyu Liang","submitted_at":"2011-07-22T01:29:00Z","abstract_excerpt":"Let $(\\mathcal{X}, d, \\mu)$ be a metric measure space, $L$ a linear operator which has a bounded $H_\\infty$ functional calculus and satisfies the Davies-Gaffney estimate, $\\Phi$ a concave function on $(0,\\infty)$ of critical lower type $p_\\Phi^-\\in(0,1]$ and $\\rho(t)\\equiv t^{-1}/\\Phi^{-1}(t^{-1})$ for all $t\\in(0,\\infty)$. In this paper, the authors introduce the generalized VMO space ${\\mathrm {VMO}}_{\\rho,L}({\\mathcal X})$ associated with $L$, and establish its characterization via the tent space. As applications, the authors show that $({\\mathrm {VMO}}_{\\rho,L}({\\mathcal X}))^*=B_{\\Phi,L^*"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4408","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":""},"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"}