{"paper":{"title":"Berezin transform and Toeplitz operators on weighted Bergman spaces induced by regular weights","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, Kian Sierra","submitted_at":"2016-07-15T07:13:50Z","abstract_excerpt":"Given a regular weight $\\omega$ and a positive Borel measure $\\mu$ on the unit disc $\\mathbb{D}$, the Toeplitz operator associated with $\\mu$ is\n  $$\n  \\mathcal{T}_\\mu(f)(z)=\\int_{\\mathbb{D}} f(\\zeta)\\bar{B_z^\\omega(\\zeta)}\\,d\\mu(\\zeta),\n  $$ where $B^\\omega_{z}$ are the reproducing kernels of the weighted Bergman space $A^2_\\omega$. We describe bounded and compact Toeplitz operators $\\mathcal{T}_\\mu:A^p_\\omega\\to A^q_\\omega$, $1<q,p<\\infty$, in terms of Carleson measures and the Berezin transform\n  $$\n  \\widetilde{\\mathcal{T}_\\mu}(z)=\\frac{\\langle\\mathcal{T}_\\mu(B^\\omega_{z}), B^\\omega_{z} \\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04394","kind":"arxiv","version":1},"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"}