{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HBQAJFPZTBJK2BJZJYHBGOMESJ","short_pith_number":"pith:HBQAJFPZ","canonical_record":{"source":{"id":"1409.0679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-02T12:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"8b1e88ae153b8df6d660e2e169e8bbd4f8e09f042afb0687d0bf81eaab97140d","abstract_canon_sha256":"0513de5c692e0cd757413cc4a2ccf5e65b244fc8ec177263f7095c1a976aa04d"},"schema_version":"1.0"},"canonical_sha256":"38600495f99852ad05394e0e133984927d63380ed98cfa4f9cf4bf9d2183db6c","source":{"kind":"arxiv","id":"1409.0679","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0679","created_at":"2026-05-18T01:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0679v2","created_at":"2026-05-18T01:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0679","created_at":"2026-05-18T01:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"HBQAJFPZTBJK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HBQAJFPZTBJK2BJZ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HBQAJFPZ","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HBQAJFPZTBJK2BJZJYHBGOMESJ","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-02T12:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"8b1e88ae153b8df6d660e2e169e8bbd4f8e09f042afb0687d0bf81eaab97140d","abstract_canon_sha256":"0513de5c692e0cd757413cc4a2ccf5e65b244fc8ec177263f7095c1a976aa04d"},"schema_version":"1.0"},"canonical_sha256":"38600495f99852ad05394e0e133984927d63380ed98cfa4f9cf4bf9d2183db6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:04.012854Z","signature_b64":"BmACOjAXwocOid0aPnSG6jdHwWGY1vnEUQ+bl4uzxVA4BJNCS/5q9lqJMy9xIAwlilo+Sk/h/KhTXLWMPdBjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38600495f99852ad05394e0e133984927d63380ed98cfa4f9cf4bf9d2183db6c","last_reissued_at":"2026-05-18T01:36:04.011987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:04.011987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0679","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":"2026-05-18T01:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSplx3R+8t9ZVJo4Ean9fBCiawyJW6t7eQVzbSFg/A8BaqyozoTXV8YlPqAaFgOGpa5i3q9a7xtrsOEkYEgMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:12:51.264630Z"},"content_sha256":"97b13b7d632a541b7d8dd1af9d2b5802958ab170711fc5312707ea0d280dad33","schema_version":"1.0","event_id":"sha256:97b13b7d632a541b7d8dd1af9d2b5802958ab170711fc5312707ea0d280dad33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HBQAJFPZTBJK2BJZJYHBGOMESJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the boundedness of singular integrals in Morrey spaces and its preduals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hans-J\\\"urgen Schmeisser, Marcel Rosenthal","submitted_at":"2014-09-02T12:22:50Z","abstract_excerpt":"We reduce the boundedness of operators in Morrey spaces $L_p^r({\\mathbb R}^n)$, its preduals, $H^{\\varrho}L_p ({\\mathbb R}^n)$, and their preduals $\\overset{\\circ}{L}{}^r_p({\\mathbb R}^n)$ to the boundedness of the appropriate operators in Lebesgue spaces, $L_p({\\mathbb R}^n)$. Hereby, we need a weak condition with respect to the operators which is satisfied for a large set of classical operators of harmonic analysis including singular integral operators and the Hardy-Littlewood maximal function. The given vector-valued consideration of these issues is a key ingredient for various applications"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0679","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":"2026-05-18T01:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6esP60cfaG4poCkvDCza2LbuDY0Fpk6FM/KfAryv/c2j+Xz1O7eQ+spQlf+6/wbZKudwjMWB1sach0aZ5xqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:12:51.264973Z"},"content_sha256":"4680e9aedd850d6df056fb7ce2893e071be85e0f478ced0e8718a1f0f5610139","schema_version":"1.0","event_id":"sha256:4680e9aedd850d6df056fb7ce2893e071be85e0f478ced0e8718a1f0f5610139"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBQAJFPZTBJK2BJZJYHBGOMESJ/bundle.json","state_url":"https://pith.science/pith/HBQAJFPZTBJK2BJZJYHBGOMESJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBQAJFPZTBJK2BJZJYHBGOMESJ/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":"2026-06-26T07:12:51Z","links":{"resolver":"https://pith.science/pith/HBQAJFPZTBJK2BJZJYHBGOMESJ","bundle":"https://pith.science/pith/HBQAJFPZTBJK2BJZJYHBGOMESJ/bundle.json","state":"https://pith.science/pith/HBQAJFPZTBJK2BJZJYHBGOMESJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBQAJFPZTBJK2BJZJYHBGOMESJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HBQAJFPZTBJK2BJZJYHBGOMESJ","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":"0513de5c692e0cd757413cc4a2ccf5e65b244fc8ec177263f7095c1a976aa04d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-02T12:22:50Z","title_canon_sha256":"8b1e88ae153b8df6d660e2e169e8bbd4f8e09f042afb0687d0bf81eaab97140d"},"schema_version":"1.0","source":{"id":"1409.0679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0679","created_at":"2026-05-18T01:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0679v2","created_at":"2026-05-18T01:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0679","created_at":"2026-05-18T01:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"HBQAJFPZTBJK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HBQAJFPZTBJK2BJZ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HBQAJFPZ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:4680e9aedd850d6df056fb7ce2893e071be85e0f478ced0e8718a1f0f5610139","target":"graph","created_at":"2026-05-18T01:36:04Z","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 reduce the boundedness of operators in Morrey spaces $L_p^r({\\mathbb R}^n)$, its preduals, $H^{\\varrho}L_p ({\\mathbb R}^n)$, and their preduals $\\overset{\\circ}{L}{}^r_p({\\mathbb R}^n)$ to the boundedness of the appropriate operators in Lebesgue spaces, $L_p({\\mathbb R}^n)$. Hereby, we need a weak condition with respect to the operators which is satisfied for a large set of classical operators of harmonic analysis including singular integral operators and the Hardy-Littlewood maximal function. The given vector-valued consideration of these issues is a key ingredient for various applications","authors_text":"Hans-J\\\"urgen Schmeisser, Marcel Rosenthal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-02T12:22:50Z","title":"On the boundedness of singular integrals in Morrey spaces and its preduals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0679","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":"sha256:97b13b7d632a541b7d8dd1af9d2b5802958ab170711fc5312707ea0d280dad33","target":"record","created_at":"2026-05-18T01:36:04Z","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":"0513de5c692e0cd757413cc4a2ccf5e65b244fc8ec177263f7095c1a976aa04d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-02T12:22:50Z","title_canon_sha256":"8b1e88ae153b8df6d660e2e169e8bbd4f8e09f042afb0687d0bf81eaab97140d"},"schema_version":"1.0","source":{"id":"1409.0679","kind":"arxiv","version":2}},"canonical_sha256":"38600495f99852ad05394e0e133984927d63380ed98cfa4f9cf4bf9d2183db6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38600495f99852ad05394e0e133984927d63380ed98cfa4f9cf4bf9d2183db6c","first_computed_at":"2026-05-18T01:36:04.011987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:04.011987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BmACOjAXwocOid0aPnSG6jdHwWGY1vnEUQ+bl4uzxVA4BJNCS/5q9lqJMy9xIAwlilo+Sk/h/KhTXLWMPdBjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:04.012854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97b13b7d632a541b7d8dd1af9d2b5802958ab170711fc5312707ea0d280dad33","sha256:4680e9aedd850d6df056fb7ce2893e071be85e0f478ced0e8718a1f0f5610139"],"state_sha256":"7a1ebe16fd04a3cbe3f45cf93be105468f4065fe78f3630cb3d9693e70d2311f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7P2uFR+v9pdjciGQ3o9WJEzH8OYj2zi4RqdsHs3M4efetMVYoHuSMOqZMI4XrvYKp63dwL9TxT1BejFLvjtFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:12:51.266861Z","bundle_sha256":"95ff94d7648ee2d8825f09cd9b2f8353f44094d53a9dd812c87219b1902c0152"}}