{"paper":{"title":"Weighted BMO spaces associated to operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"The Anh Bui, Xuan Thinh Duong","submitted_at":"2012-01-27T16:46:52Z","abstract_excerpt":"Let $X$ be a metric space equipped with a metric $d$ and a nonnegative Borel measure $\\mu$ satisfying the doubling property and let $\\{\\mathcal{A}_t\\}_{t>0}$, be a generalized approximations to the identity, for example $\\{\\mathcal{A}_t\\}$ is a holomorphic semigroup $e^{-tL}$ with Gaussian upper bounds generated by an operators $L$ on $L^2(X)$. In this paper, we introduce and study the weighted BMO space BMO$_\\mathcal{A}(X,w)$ associated to the the family \\{\\mathcal{A}_t\\}$. We show that for these spaces, the weighted John-Nirenberg inequality holds and we establish an interpolation theorem in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5828","kind":"arxiv","version":3},"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"}