{"paper":{"title":"Two weight inequality for Bergman projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2014-06-11T10:42:49Z","abstract_excerpt":"The motivation of this paper comes from the two weight inequality $$\\|P_\\omega(f)\\|_{L^p_v}\\le C\\|f\\|_{L^p_v},\\quad f\\in L^p_v,$$ for the Bergman projection $P_\\omega$ in the unit disc. We show that the boundedness of $P_\\omega$ on $L^p_v$ is characterized in terms of self-improving Muckenhoupt and Bekoll\\'e-Bonami type conditions when the radial weights $v$ and $\\omega$ admit certain smoothness. En route to the proof we describe the asymptotic behavior of the $L^p$-means and the $L^p_v$-integrability of the reproducing kernels of the weighted Bergman space $A^2_\\omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2857","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"}