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Mart\\'in Reyes, Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a, Pedro Ortega","submitted_at":"2021-05-17T17:28:29Z","abstract_excerpt":"Let $\\omega$ and $\\nu$ be radial weights on the unit disc of the complex plane such that $\\omega$ admits the doubling property $\\sup_{0\\le r<1}\\frac{\\int_r^1 \\omega(s)\\,ds}{\\int_{\\frac{1+r}{2}}^1 \\omega(s)\\,ds}<\\infty$. Consider the one weight inequality\n  \\begin{equation}\\label{ab1}\n  \\|P_\\omega(f)\\|_{L^p_\\nu}\\le C\\|f\\|_{L^p_\\nu},\\quad 1<p<\\infty,\\tag{\\dag}\n  \\end{equation} for the Bergman projection $P_\\omega$ induced by $\\omega$. It is shown that the Muckenhoupt-type condition\n  $$\n  A_p(\\omega,\\nu)=\\sup_{0\\le r<1}\\frac{\\left(\\int_r^1 s\\nu(s)\\,ds \\right)^{\\frac{1}{p}}\\left(\\int_r^1 s\\left(\\"},"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":"2105.08029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2021-05-17T17:28:29Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"644b7ae2777a41d1764600a8ba3c91435e4afe1763647521cb88b87cd17b219c","abstract_canon_sha256":"2fb0800fb5ec0ab2df8db9c5ef3b2f94904f48e63aee31d60ab28ceca8ffb99a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:40:47.154811Z","signature_b64":"34I9luj1C/wurYDHLs2GSu3Ld/st5R/Jvs3o+070yb/hzxGzQmxVrWoE8euM03o2GYXHSS206cyTHtpbkyn/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"476bd2eaabd4b505ecef8586c5aade5b2dc0eacc872597d452705448c0876f20","last_reissued_at":"2026-07-05T02:40:47.154301Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:40:47.154301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One weight inequality for Bergman projection and Calder\\'on operator induced by radial weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Francisco J. Mart\\'in Reyes, Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a, Pedro Ortega","submitted_at":"2021-05-17T17:28:29Z","abstract_excerpt":"Let $\\omega$ and $\\nu$ be radial weights on the unit disc of the complex plane such that $\\omega$ admits the doubling property $\\sup_{0\\le r<1}\\frac{\\int_r^1 \\omega(s)\\,ds}{\\int_{\\frac{1+r}{2}}^1 \\omega(s)\\,ds}<\\infty$. Consider the one weight inequality\n  \\begin{equation}\\label{ab1}\n  \\|P_\\omega(f)\\|_{L^p_\\nu}\\le C\\|f\\|_{L^p_\\nu},\\quad 1<p<\\infty,\\tag{\\dag}\n  \\end{equation} for the Bergman projection $P_\\omega$ induced by $\\omega$. It is shown that the Muckenhoupt-type condition\n  $$\n  A_p(\\omega,\\nu)=\\sup_{0\\le r<1}\\frac{\\left(\\int_r^1 s\\nu(s)\\,ds \\right)^{\\frac{1}{p}}\\left(\\int_r^1 s\\left(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08029","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.08029/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2105.08029","created_at":"2026-07-05T02:40:47.154367+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.08029v1","created_at":"2026-07-05T02:40:47.154367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08029","created_at":"2026-07-05T02:40:47.154367+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5V5F2VL2S2Q","created_at":"2026-07-05T02:40:47.154367+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5V5F2VL2S2QL3HP","created_at":"2026-07-05T02:40:47.154367+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5V5F2VL","created_at":"2026-07-05T02:40:47.154367+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.19862","citing_title":"Two weights inequality for Hankel operators on weighted Bergman spaces induced by radial weights","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM","json":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM.json","graph_json":"https://pith.science/api/pith-number/I5V5F2VL2S2QL3HPQWDMLKW6LM/graph.json","events_json":"https://pith.science/api/pith-number/I5V5F2VL2S2QL3HPQWDMLKW6LM/events.json","paper":"https://pith.science/paper/I5V5F2VL"},"agent_actions":{"view_html":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM","download_json":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM.json","view_paper":"https://pith.science/paper/I5V5F2VL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.08029&json=true","fetch_graph":"https://pith.science/api/pith-number/I5V5F2VL2S2QL3HPQWDMLKW6LM/graph.json","fetch_events":"https://pith.science/api/pith-number/I5V5F2VL2S2QL3HPQWDMLKW6LM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM/action/storage_attestation","attest_author":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM/action/author_attestation","sign_citation":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM/action/citation_signature","submit_replication":"https://pith.science/pith/I5V5F2VL2S2QL3HPQWDMLKW6LM/action/replication_record"}},"created_at":"2026-07-05T02:40:47.154367+00:00","updated_at":"2026-07-05T02:40:47.154367+00:00"}