{"paper":{"title":"Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Zengyan Si","submitted_at":"2012-03-20T12:24:18Z","abstract_excerpt":"Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(R^n)$ with Gaussican kernel bounds, and let $L^{-\\alpha/2}$ be the fractional integrals of $L$ for $0<\\alpha<n.$ For any locally integrable function $b$, The commutators associated with $L^{-\\alpha/2}$ are defined by $[b,L^{-\\alpha/2}](f)(x)=b(x)L^{-\\alpha/2}(f)(x)-L^{-\\alpha/2}(bf)(x)$. When $b\\in BMO(\\omega)$(weighted $BMO$ space) or $b\\in BMO$, the author obtain the necessary and sufficient conditions for the boundedness of $[b,L^{-\\alpha/2}]$ on weighted Morrey spaces respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4407","kind":"arxiv","version":2},"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"}