{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B67JEDIFA7SA7BO224INUKMIG5","short_pith_number":"pith:B67JEDIF","canonical_record":{"source":{"id":"1705.04050","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-11T07:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"9da14a1b03bcb1374c2bc81a4cf4acb92f40359f5dee891e1d7bba140d61a339","abstract_canon_sha256":"eddc11c770627ccc8b44736522498b8193669b99c92b21b06b87a16b76f1e3b6"},"schema_version":"1.0"},"canonical_sha256":"0fbe920d0507e40f85dad710da298837443591bb38864fd71b1472b3223d57c6","source":{"kind":"arxiv","id":"1705.04050","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04050","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04050v2","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04050","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"B67JEDIFA7SA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B67JEDIFA7SA7BO2","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B67JEDIF","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B67JEDIFA7SA7BO224INUKMIG5","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04050","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-11T07:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"9da14a1b03bcb1374c2bc81a4cf4acb92f40359f5dee891e1d7bba140d61a339","abstract_canon_sha256":"eddc11c770627ccc8b44736522498b8193669b99c92b21b06b87a16b76f1e3b6"},"schema_version":"1.0"},"canonical_sha256":"0fbe920d0507e40f85dad710da298837443591bb38864fd71b1472b3223d57c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:08.932049Z","signature_b64":"Dkvrkjob3G0xnHv86S8Vzk/9XmaPzSxJtwRSspc5TypDPFHXxUc1GEx3IzLHPnORZzhG29UIAnn+yyqi0BmqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fbe920d0507e40f85dad710da298837443591bb38864fd71b1472b3223d57c6","last_reissued_at":"2026-05-18T00:23:08.931470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:08.931470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04050","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":"2026-05-18T00:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ViW8kdKyvtDrXHjxFESA8v2ySCV3dzrAkzzVc7tEMVq0gOCvyNqqMvO+qbkHjroOCj9iV+30yi745rS3oK0aDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:30:35.191025Z"},"content_sha256":"83ee3dbdd41717169a891d15625862b8314577d8f8128e3e5690470b6e93a3ce","schema_version":"1.0","event_id":"sha256:83ee3dbdd41717169a891d15625862b8314577d8f8128e3e5690470b6e93a3ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B67JEDIFA7SA7BO224INUKMIG5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Norm estimates for Bessel-Riesz operators on generalized Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eridani, Hendra Gunawan, Mochammad Idris","submitted_at":"2017-05-11T07:45:13Z","abstract_excerpt":"We revisit the properties of Bessel-Riesz operators and refine the proof of the boundedness of these operators on generalized Morrey spaces using Young's inequality. We also obtain an estimate for the norm of these operators on generalized Morrey spaces. In addition, we reprove the boundedness of fractional integral operators on generalized Morrey spaces and estimate their norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04050","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":"2026-05-18T00:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQXMDr3hljtIfaMX/2oMvPyGtqbtxUsJbiQYoG1Gwcz0OphnMxRem3qtAfa31PtgUsfjYoqz+JRVv44Du8y4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:30:35.191391Z"},"content_sha256":"f5cadc6e563a212ebb38e2e1e6bd129844f2e76e2907b5dbc2eba9402f10f01d","schema_version":"1.0","event_id":"sha256:f5cadc6e563a212ebb38e2e1e6bd129844f2e76e2907b5dbc2eba9402f10f01d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B67JEDIFA7SA7BO224INUKMIG5/bundle.json","state_url":"https://pith.science/pith/B67JEDIFA7SA7BO224INUKMIG5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B67JEDIFA7SA7BO224INUKMIG5/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":"2026-06-10T18:30:35Z","links":{"resolver":"https://pith.science/pith/B67JEDIFA7SA7BO224INUKMIG5","bundle":"https://pith.science/pith/B67JEDIFA7SA7BO224INUKMIG5/bundle.json","state":"https://pith.science/pith/B67JEDIFA7SA7BO224INUKMIG5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B67JEDIFA7SA7BO224INUKMIG5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B67JEDIFA7SA7BO224INUKMIG5","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":"eddc11c770627ccc8b44736522498b8193669b99c92b21b06b87a16b76f1e3b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-11T07:45:13Z","title_canon_sha256":"9da14a1b03bcb1374c2bc81a4cf4acb92f40359f5dee891e1d7bba140d61a339"},"schema_version":"1.0","source":{"id":"1705.04050","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04050","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04050v2","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04050","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"B67JEDIFA7SA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B67JEDIFA7SA7BO2","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B67JEDIF","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:f5cadc6e563a212ebb38e2e1e6bd129844f2e76e2907b5dbc2eba9402f10f01d","target":"graph","created_at":"2026-05-18T00:23:08Z","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":"We revisit the properties of Bessel-Riesz operators and refine the proof of the boundedness of these operators on generalized Morrey spaces using Young's inequality. We also obtain an estimate for the norm of these operators on generalized Morrey spaces. In addition, we reprove the boundedness of fractional integral operators on generalized Morrey spaces and estimate their norm.","authors_text":"Eridani, Hendra Gunawan, Mochammad Idris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-11T07:45:13Z","title":"Norm estimates for Bessel-Riesz operators on generalized Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04050","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":"sha256:83ee3dbdd41717169a891d15625862b8314577d8f8128e3e5690470b6e93a3ce","target":"record","created_at":"2026-05-18T00:23:08Z","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":"eddc11c770627ccc8b44736522498b8193669b99c92b21b06b87a16b76f1e3b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-11T07:45:13Z","title_canon_sha256":"9da14a1b03bcb1374c2bc81a4cf4acb92f40359f5dee891e1d7bba140d61a339"},"schema_version":"1.0","source":{"id":"1705.04050","kind":"arxiv","version":2}},"canonical_sha256":"0fbe920d0507e40f85dad710da298837443591bb38864fd71b1472b3223d57c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fbe920d0507e40f85dad710da298837443591bb38864fd71b1472b3223d57c6","first_computed_at":"2026-05-18T00:23:08.931470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:08.931470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dkvrkjob3G0xnHv86S8Vzk/9XmaPzSxJtwRSspc5TypDPFHXxUc1GEx3IzLHPnORZzhG29UIAnn+yyqi0BmqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:08.932049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04050","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83ee3dbdd41717169a891d15625862b8314577d8f8128e3e5690470b6e93a3ce","sha256:f5cadc6e563a212ebb38e2e1e6bd129844f2e76e2907b5dbc2eba9402f10f01d"],"state_sha256":"dfdba80f2734805328d6640dceabdbb0ebb6d32b4fc1907dd199eb0f033fe2a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUct8HxXRrBtGShEzEydxIwXZZ5zxQJ77DNPLlSaEIcr7N/w7+/qhnLQq7dGxHtkdxHxfNEUQDNiqCN5jo5oDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:30:35.193343Z","bundle_sha256":"8cab4cc54e8707259b9a144aa0b94d1d56bead4ae978a365294a7383431e1688"}}