{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5X32OT2ETDUAAZSAX6ULYF7NMY","short_pith_number":"pith:5X32OT2E","canonical_record":{"source":{"id":"1707.07492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-24T11:25:20Z","cross_cats_sorted":[],"title_canon_sha256":"66ad23bb1f26815dcd2f012bd8eab8ed6a04a0dd5e88956b88f61047e20976c3","abstract_canon_sha256":"ea4c06e74a95fcea5b698a93fae44eb1bb7652a0009e275e08866dc58e566cec"},"schema_version":"1.0"},"canonical_sha256":"edf7a74f4498e8006640bfa8bc17ed6623ff1e3c2509750d37e4c28e9d5e5a7a","source":{"kind":"arxiv","id":"1707.07492","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07492","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07492v2","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07492","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"5X32OT2ETDUA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5X32OT2ETDUAAZSA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5X32OT2E","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5X32OT2ETDUAAZSAX6ULYF7NMY","target":"record","payload":{"canonical_record":{"source":{"id":"1707.07492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-24T11:25:20Z","cross_cats_sorted":[],"title_canon_sha256":"66ad23bb1f26815dcd2f012bd8eab8ed6a04a0dd5e88956b88f61047e20976c3","abstract_canon_sha256":"ea4c06e74a95fcea5b698a93fae44eb1bb7652a0009e275e08866dc58e566cec"},"schema_version":"1.0"},"canonical_sha256":"edf7a74f4498e8006640bfa8bc17ed6623ff1e3c2509750d37e4c28e9d5e5a7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:44.517972Z","signature_b64":"KmKCExmFCxBxxWEfSfQjhcvTbKf5Ismcs2yZHeWIUTiAaLTwsNkCU5i8aO8AH1xZzMeltJuVTk96v/O1e85+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edf7a74f4498e8006640bfa8bc17ed6623ff1e3c2509750d37e4c28e9d5e5a7a","last_reissued_at":"2026-05-17T23:52:44.517500Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:44.517500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.07492","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grINxw1mPXSnihYTOnxUwMi5vqCX8ziUTCkr9Zo2fD4g0XOk55KnLivbsujB19UY5+YGPSHNWFUv57QREXZUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:49:13.627880Z"},"content_sha256":"30119e27053a78e67a97a65304b84bb47d9d348f477a91d9463964b1d149223f","schema_version":"1.0","event_id":"sha256:30119e27053a78e67a97a65304b84bb47d9d348f477a91d9463964b1d149223f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5X32OT2ETDUAAZSAX6ULYF7NMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Two-Weight Inequality for the Poisson Operator in the Bessel Setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Brett D. Wick, Ji Li","submitted_at":"2017-07-24T11:25:20Z","abstract_excerpt":"Fix $\\lambda>0$. Consider the Bessel operator $\\Delta_\\lambda:=-\\frac{d^2}{dx^2}-\\frac{2\\lambda}{x}\\frac d{dx}$ on $\\mathbb{R}_+:=(0,\\infty)$ and the harmonic conjugacy introduced by Muckenhoupt and Stein. We provide the two-weight inequality for the Poisson operator $\\mathsf{P}^{[\\lambda]}_t=e^{-t\\sqrt{\\Delta_\\lambda}}$ in this Bessel setting. In particular, we prove that for a measure $\\mu$ on $\\mathbb{R}^2_{+,+}:=(0,\\infty)\\times (0,\\infty)$ and $\\sigma$ on $\\mathbb{R}_+$: $$ \\|\\mathsf{P}^{[\\lambda]}_\\sigma(f)\\|_{L^2(\\mathbb{R}^2_{+,+};\\mu)} \\lesssim \\|f\\|_{L^2(\\mathbb{R}_+;\\sigma)}, $$ if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07492","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWt3U0mIrJgCv1slH6nZyuLc+g8qyMHByrLX5IQZH1P39IkIi1IzjVkY7KkSm6voyoZ/97OB8ds+FCejTjoFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:49:13.628247Z"},"content_sha256":"c496631f18d12217f3964e0a0c07e7329298e048c8d7462491cddad98c60d74a","schema_version":"1.0","event_id":"sha256:c496631f18d12217f3964e0a0c07e7329298e048c8d7462491cddad98c60d74a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5X32OT2ETDUAAZSAX6ULYF7NMY/bundle.json","state_url":"https://pith.science/pith/5X32OT2ETDUAAZSAX6ULYF7NMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5X32OT2ETDUAAZSAX6ULYF7NMY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T07:49:13Z","links":{"resolver":"https://pith.science/pith/5X32OT2ETDUAAZSAX6ULYF7NMY","bundle":"https://pith.science/pith/5X32OT2ETDUAAZSAX6ULYF7NMY/bundle.json","state":"https://pith.science/pith/5X32OT2ETDUAAZSAX6ULYF7NMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5X32OT2ETDUAAZSAX6ULYF7NMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5X32OT2ETDUAAZSAX6ULYF7NMY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ea4c06e74a95fcea5b698a93fae44eb1bb7652a0009e275e08866dc58e566cec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-24T11:25:20Z","title_canon_sha256":"66ad23bb1f26815dcd2f012bd8eab8ed6a04a0dd5e88956b88f61047e20976c3"},"schema_version":"1.0","source":{"id":"1707.07492","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07492","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07492v2","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07492","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"5X32OT2ETDUA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5X32OT2ETDUAAZSA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5X32OT2E","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:c496631f18d12217f3964e0a0c07e7329298e048c8d7462491cddad98c60d74a","target":"graph","created_at":"2026-05-17T23:52:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Fix $\\lambda>0$. Consider the Bessel operator $\\Delta_\\lambda:=-\\frac{d^2}{dx^2}-\\frac{2\\lambda}{x}\\frac d{dx}$ on $\\mathbb{R}_+:=(0,\\infty)$ and the harmonic conjugacy introduced by Muckenhoupt and Stein. We provide the two-weight inequality for the Poisson operator $\\mathsf{P}^{[\\lambda]}_t=e^{-t\\sqrt{\\Delta_\\lambda}}$ in this Bessel setting. In particular, we prove that for a measure $\\mu$ on $\\mathbb{R}^2_{+,+}:=(0,\\infty)\\times (0,\\infty)$ and $\\sigma$ on $\\mathbb{R}_+$: $$ \\|\\mathsf{P}^{[\\lambda]}_\\sigma(f)\\|_{L^2(\\mathbb{R}^2_{+,+};\\mu)} \\lesssim \\|f\\|_{L^2(\\mathbb{R}_+;\\sigma)}, $$ if ","authors_text":"Brett D. Wick, Ji Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-24T11:25:20Z","title":"The Two-Weight Inequality for the Poisson Operator in the Bessel Setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07492","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:30119e27053a78e67a97a65304b84bb47d9d348f477a91d9463964b1d149223f","target":"record","created_at":"2026-05-17T23:52:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ea4c06e74a95fcea5b698a93fae44eb1bb7652a0009e275e08866dc58e566cec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-24T11:25:20Z","title_canon_sha256":"66ad23bb1f26815dcd2f012bd8eab8ed6a04a0dd5e88956b88f61047e20976c3"},"schema_version":"1.0","source":{"id":"1707.07492","kind":"arxiv","version":2}},"canonical_sha256":"edf7a74f4498e8006640bfa8bc17ed6623ff1e3c2509750d37e4c28e9d5e5a7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf7a74f4498e8006640bfa8bc17ed6623ff1e3c2509750d37e4c28e9d5e5a7a","first_computed_at":"2026-05-17T23:52:44.517500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:44.517500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KmKCExmFCxBxxWEfSfQjhcvTbKf5Ismcs2yZHeWIUTiAaLTwsNkCU5i8aO8AH1xZzMeltJuVTk96v/O1e85+CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:44.517972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07492","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30119e27053a78e67a97a65304b84bb47d9d348f477a91d9463964b1d149223f","sha256:c496631f18d12217f3964e0a0c07e7329298e048c8d7462491cddad98c60d74a"],"state_sha256":"5470b75ae54eab83c9b55f126ee8e00a18b6ce9bb3f5f0555ee4ec0fd598634d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oU0AZGyyS7g0aADxblROZGoFGiG5yc4LtxkacZO7ThEL7l0ZKeBUbWSa0DqZ0bjmXfo0lKAWcoRnEHY+WwM0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:49:13.630192Z","bundle_sha256":"89048aa4cc69cb28878aa4a5683affce116d1bca8e310f97180d8e492f96591b"}}