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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.01639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-06T05:08:03Z","cross_cats_sorted":[],"title_canon_sha256":"4bca886ba0cdc6b5a877b027eaedf4b940a61ae4dd4768c428c56b6abd984bbe","abstract_canon_sha256":"06de7b37e1277aa9ef1dea65566d73bbdd3e35fa10d444a2d7886071e88dbd1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:47.987620Z","signature_b64":"1QPbkiH976Yl0Lg5BTihGfe1IetKWzKKkjA4sotORWGEc/8wT16+DQdr2bkhqMCEhPshNYDqDr4yp0+vNGHsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"923760952f5ed076bfd7b5e467c7c21fb9b43c0c407b8d7764300310cd4cee05","last_reissued_at":"2026-05-18T00:40:47.986938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:47.986938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $L^{p,\\infty}(\\omega)$. 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