{"paper":{"title":"Bergman projection induced by kernel with integral representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Brett D. Wick, Jos\\'e A. Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2016-06-02T15:24:05Z","abstract_excerpt":"Bounded Bergman projections $P_\\omega:L^p_\\omega(v)\\to L^p_\\omega(v)$, induced by reproducing kernels admitting the representation\n  $$\n  \\frac{1}{(1-\\overline{z}\\zeta)^\\gamma}\\int_0^1\\frac{d\\nu(r)}{1-r\\overline{z}\\zeta},\n  $$ and the corresponding (1,1)-inequality are characterized in terms of Bekoll\\'e-Bonami-type conditions. The two-weight inequality for the maximal Bergman projection $P^+_\\omega:L^p_\\omega(u)\\to L^p_\\omega(v)$ in terms of Sawyer-testing conditions is also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00718","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"}