{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZIEQXWKQ5FOIPJO6L624LQZGYK","short_pith_number":"pith:ZIEQXWKQ","canonical_record":{"source":{"id":"1110.2348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-11T12:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"bf1b67906b25bfb38fa77c8e8beb3eefed814c96a2d4fe846b94cd39457056cc","abstract_canon_sha256":"6afd8a81be9a49fe2950e0747d34ae31be9c45efc9ced9a8ae9a20ec2955b3e7"},"schema_version":"1.0"},"canonical_sha256":"ca090bd950e95c87a5de5fb5c5c326c2a21768e13d2e56bd74db3533ceb80399","source":{"kind":"arxiv","id":"1110.2348","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2348","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2348v2","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2348","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZIEQXWKQ5FOI","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZIEQXWKQ5FOIPJO6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZIEQXWKQ","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZIEQXWKQ5FOIPJO6L624LQZGYK","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-11T12:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"bf1b67906b25bfb38fa77c8e8beb3eefed814c96a2d4fe846b94cd39457056cc","abstract_canon_sha256":"6afd8a81be9a49fe2950e0747d34ae31be9c45efc9ced9a8ae9a20ec2955b3e7"},"schema_version":"1.0"},"canonical_sha256":"ca090bd950e95c87a5de5fb5c5c326c2a21768e13d2e56bd74db3533ceb80399","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:07.541508Z","signature_b64":"yXBHbL19iHrtc9eek7hhNPuckE4CIAWPCzn6QiJy68RoVoiEStxEyO3ct3J3LtQvxgzQIkJp1sYApfCmGMmeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca090bd950e95c87a5de5fb5c5c326c2a21768e13d2e56bd74db3533ceb80399","last_reissued_at":"2026-05-18T04:06:07.541001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:07.541001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2348","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":"2026-05-18T04:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evtRC14CmfyynVRxGiFl3yB+EamXWS7LJO+gFWObwTvlGV3y0Ic6bEIIuHdrACDAajPhTU32Q3sukb9L8IAXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:52:26.119868Z"},"content_sha256":"201e1fe3b988253df8f13b76d3d408f17af3554c4f67d7b4869bcc0b0b74a93c","schema_version":"1.0","event_id":"sha256:201e1fe3b988253df8f13b76d3d408f17af3554c4f67d7b4869bcc0b0b74a93c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZIEQXWKQ5FOIPJO6L624LQZGYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate H\\\"ormander-type multiplier theorem for the Hankel transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Jacek Dziuba\\'nski, Marcin Preisner","submitted_at":"2011-10-11T12:30:02Z","abstract_excerpt":"Let H(f)(x)=\\int_{(0,infty)^d} f(v) E_{x}(v) d\\nu(v), be the multivariable Hankel transform, where E_{x}(v)=\\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), d\\nu(v)=v^a dv, a=(a_1,...,a_d). We give sufficient conditions on a bounded continuous function m(v) which guarantee that the operator H(m Hf) is bounded on L^p(d\\nu) and of weak-type (1,1), or bounded on the Hardy space H^1((0,infty)^d, d\\nu) in the sense of Coifman-Weiss."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2348","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":"2026-05-18T04:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OtDDyCjlBo8xtYZPdNFQEFFVuB/bBU17BVTwAN9Wd43z6TPVeMX37osy0UpRFNtI5+5h7mqX0pddq4XkwDrFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:52:26.120449Z"},"content_sha256":"4e4d9d7ee3e99ad11a2ed7c1f4cbb142db77c9bfbcabeddfa9405b01ba152d2d","schema_version":"1.0","event_id":"sha256:4e4d9d7ee3e99ad11a2ed7c1f4cbb142db77c9bfbcabeddfa9405b01ba152d2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/bundle.json","state_url":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/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":"2026-06-03T14:52:26Z","links":{"resolver":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK","bundle":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/bundle.json","state":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZIEQXWKQ5FOIPJO6L624LQZGYK","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":"6afd8a81be9a49fe2950e0747d34ae31be9c45efc9ced9a8ae9a20ec2955b3e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-11T12:30:02Z","title_canon_sha256":"bf1b67906b25bfb38fa77c8e8beb3eefed814c96a2d4fe846b94cd39457056cc"},"schema_version":"1.0","source":{"id":"1110.2348","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2348","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2348v2","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2348","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZIEQXWKQ5FOI","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZIEQXWKQ5FOIPJO6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZIEQXWKQ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:4e4d9d7ee3e99ad11a2ed7c1f4cbb142db77c9bfbcabeddfa9405b01ba152d2d","target":"graph","created_at":"2026-05-18T04:06:07Z","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":"Let H(f)(x)=\\int_{(0,infty)^d} f(v) E_{x}(v) d\\nu(v), be the multivariable Hankel transform, where E_{x}(v)=\\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), d\\nu(v)=v^a dv, a=(a_1,...,a_d). We give sufficient conditions on a bounded continuous function m(v) which guarantee that the operator H(m Hf) is bounded on L^p(d\\nu) and of weak-type (1,1), or bounded on the Hardy space H^1((0,infty)^d, d\\nu) in the sense of Coifman-Weiss.","authors_text":"B{\\l}a\\.zej Wr\\'obel, Jacek Dziuba\\'nski, Marcin Preisner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-11T12:30:02Z","title":"Multivariate H\\\"ormander-type multiplier theorem for the Hankel transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2348","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":"sha256:201e1fe3b988253df8f13b76d3d408f17af3554c4f67d7b4869bcc0b0b74a93c","target":"record","created_at":"2026-05-18T04:06:07Z","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":"6afd8a81be9a49fe2950e0747d34ae31be9c45efc9ced9a8ae9a20ec2955b3e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-11T12:30:02Z","title_canon_sha256":"bf1b67906b25bfb38fa77c8e8beb3eefed814c96a2d4fe846b94cd39457056cc"},"schema_version":"1.0","source":{"id":"1110.2348","kind":"arxiv","version":2}},"canonical_sha256":"ca090bd950e95c87a5de5fb5c5c326c2a21768e13d2e56bd74db3533ceb80399","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca090bd950e95c87a5de5fb5c5c326c2a21768e13d2e56bd74db3533ceb80399","first_computed_at":"2026-05-18T04:06:07.541001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:07.541001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yXBHbL19iHrtc9eek7hhNPuckE4CIAWPCzn6QiJy68RoVoiEStxEyO3ct3J3LtQvxgzQIkJp1sYApfCmGMmeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:07.541508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2348","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:201e1fe3b988253df8f13b76d3d408f17af3554c4f67d7b4869bcc0b0b74a93c","sha256:4e4d9d7ee3e99ad11a2ed7c1f4cbb142db77c9bfbcabeddfa9405b01ba152d2d"],"state_sha256":"96676c40ca925a715a868f1e92ce0ed11183dfabe04e7fa8d267fae61ed7ed9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uvU0cKoEL9CCZRg5233j8Fh7QDgQMB4anOYQzXAUiC7/a3ygnxHGc+9RsSsqKpeZ6Mf/aQQi3cIzCRWDFik8Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:52:26.123094Z","bundle_sha256":"b36ab8ac38780a561faa6f0bcb6e91015c29ce569197ed511823bf34d0f6d479"}}