{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:B4ZCEIMUNS4FOEM6G3JMDNJLYN","short_pith_number":"pith:B4ZCEIMU","schema_version":"1.0","canonical_sha256":"0f322221946cb857119e36d2c1b52bc345763382a46e125175840f71772185b7","source":{"kind":"arxiv","id":"1607.04394","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.04394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-15T07:13:50Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"cba276409312013819e4737dfcaf248012f99144a8c17a903e2d75885d374b20","abstract_canon_sha256":"878400f7bfca7059ca48faa3fda44c7e53b35a0ccea6be14e4f83626bb1d3d06"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:01.335031Z","signature_b64":"swb07Z+spesU+b080FcD+YMGFZSL/QmamhFwf3LiUfbLTiYBwlmSw/2/Y7aYWefZwtZRuX0mDBdFHGSu1Q/1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f322221946cb857119e36d2c1b52bc345763382a46e125175840f71772185b7","last_reissued_at":"2026-05-18T01:11:01.334516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:01.334516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.04394","created_at":"2026-05-18T01:11:01.334600+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.04394v1","created_at":"2026-05-18T01:11:01.334600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04394","created_at":"2026-05-18T01:11:01.334600+00:00"},{"alias_kind":"pith_short_12","alias_value":"B4ZCEIMUNS4F","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"B4ZCEIMUNS4FOEM6","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"B4ZCEIMU","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN","json":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN.json","graph_json":"https://pith.science/api/pith-number/B4ZCEIMUNS4FOEM6G3JMDNJLYN/graph.json","events_json":"https://pith.science/api/pith-number/B4ZCEIMUNS4FOEM6G3JMDNJLYN/events.json","paper":"https://pith.science/paper/B4ZCEIMU"},"agent_actions":{"view_html":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN","download_json":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN.json","view_paper":"https://pith.science/paper/B4ZCEIMU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.04394&json=true","fetch_graph":"https://pith.science/api/pith-number/B4ZCEIMUNS4FOEM6G3JMDNJLYN/graph.json","fetch_events":"https://pith.science/api/pith-number/B4ZCEIMUNS4FOEM6G3JMDNJLYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN/action/storage_attestation","attest_author":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN/action/author_attestation","sign_citation":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN/action/citation_signature","submit_replication":"https://pith.science/pith/B4ZCEIMUNS4FOEM6G3JMDNJLYN/action/replication_record"}},"created_at":"2026-05-18T01:11:01.334600+00:00","updated_at":"2026-05-18T01:11:01.334600+00:00"}