{"paper":{"title":"Characterizations of weighted BMO space and its application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinghuai Wang, Jiang Zhou, Zhidong Teng","submitted_at":"2017-07-06T05:08:03Z","abstract_excerpt":"In this paper, we prove that the weighted BMO space as follows $${\\rm BMO}^{p}(\\omega)=\\Big\\{f\\in L^{1}_{\\rm loc}:\\sup_{Q}\\|\\chi_{Q}\\|^{-1}_{L^{p}(\\omega)}\\big\\|(f-f_{Q})\\omega^{-1}\\chi_{Q}\\big\\|_{L^{p}(\\omega)}<\\infty\\Big\\}$$ is independent of the scale $p\\in (0,\\infty)$ in sense of norm when $\\omega\\in A_{1}$. Moreover, we can replace $L^{p}(\\omega)$ by $L^{p,\\infty}(\\omega)$. As an application, we characterize this space by the boundedness of the bilinear commutators $[b,T]_{j} (j=1,2)$, generated by the bilinear convolution type Calder\\'{o}n-Zygmund operators and the symbol $b$, from $L^{p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01639","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"}