{"paper":{"title":"Weighted little bmo and two-weight inequalities for Journ\\'e commutators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Irina Holmes, Stefanie Petermichl","submitted_at":"2017-01-23T17:51:08Z","abstract_excerpt":"We characterize the boundedness of the commutators $[b, T]$ with biparameter Journ\\'{e} operators $T$ in the two-weight, Bloom-type setting, and express the norms of these commutators in terms of a weighted little $bmo$ norm of the symbol $b$. Specifically, if $\\mu$ and $\\lambda$ are biparameter $A_p$ weights, $\\nu := \\mu^{1/p}\\lambda^{-1/p}$ is the Bloom weight, and $b$ is in $bmo(\\nu)$, then we prove a lower bound and testing condition $\\|b\\|_{bmo(\\nu)} \\lesssim \\sup \\| [b, R_k^1 R_l^2]: L^p(\\mu) \\rightarrow L^p(\\lambda)\\|$, where $R_k^1$ and $R_l^2$ are Riesz transforms acting in each varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06526","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"}