{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OEU6RT7OOWQBOW3YOTE3FNARXW","short_pith_number":"pith:OEU6RT7O","canonical_record":{"source":{"id":"2110.01193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-10-04T05:23:27Z","cross_cats_sorted":[],"title_canon_sha256":"e3a6d757bc322fd5d5350bc7f1b39bed1b26249030e659372d72f88874d981df","abstract_canon_sha256":"45725333b06b001693bdcb01735221e4895c8f6ba5e39da0e1816ea10a6b9651"},"schema_version":"1.0"},"canonical_sha256":"7129e8cfee75a0175b7874c9b2b411bdbea7540246328a99aa88c303ab381ee9","source":{"kind":"arxiv","id":"2110.01193","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.01193","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"2110.01193v1","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.01193","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"OEU6RT7OOWQB","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"OEU6RT7OOWQBOW3Y","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"OEU6RT7O","created_at":"2026-07-05T03:19:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OEU6RT7OOWQBOW3YOTE3FNARXW","target":"record","payload":{"canonical_record":{"source":{"id":"2110.01193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-10-04T05:23:27Z","cross_cats_sorted":[],"title_canon_sha256":"e3a6d757bc322fd5d5350bc7f1b39bed1b26249030e659372d72f88874d981df","abstract_canon_sha256":"45725333b06b001693bdcb01735221e4895c8f6ba5e39da0e1816ea10a6b9651"},"schema_version":"1.0"},"canonical_sha256":"7129e8cfee75a0175b7874c9b2b411bdbea7540246328a99aa88c303ab381ee9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:19:52.805149Z","signature_b64":"XFmWwCjoOg01mOohWwpWk7QYsZETmaR0Yhh6m+pZnhlmTFb1IgiqYiPJV7+Rmn4WcMNWnmaRI28Z0VrBAQxwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7129e8cfee75a0175b7874c9b2b411bdbea7540246328a99aa88c303ab381ee9","last_reissued_at":"2026-07-05T03:19:52.804794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:19:52.804794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.01193","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p31YR+JkB908wid0Th/n/pj73S4hrF9G2PAPFA7ogu7Vd3uLfnGYVaSns6Ni7rSLZ2NQXfYGXmkBFKrX7kzHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:17:36.977707Z"},"content_sha256":"b3d21ba11582f4116da91e069e97b00bc195af0fa39973deb85c65f548fb0506","schema_version":"1.0","event_id":"sha256:b3d21ba11582f4116da91e069e97b00bc195af0fa39973deb85c65f548fb0506"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OEU6RT7OOWQBOW3YOTE3FNARXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundedness of some operators on weighted amalgam spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jiang Zhou, Songbai Wang, Yuan Lu","submitted_at":"2021-10-04T05:23:27Z","abstract_excerpt":"Let $t\\in(0,\\infty)$, $p\\in(1,\\infty)$, $q\\in[1,\\infty]$, $w\\in A_p$ and $v\\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical operators in harmonic analysis, such as the Hardy--Littlewood maximal operator, the Calder\\'on--Zygmund operator, the Riesz potential, singular integral operators with the rough kernel, the Marcinkiewicz integral, the Bochner-Riesz operator, the Littlewood-Paley $g$ function and the intrinsic square function, are considered. Our main method is extrapolation. We obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.01193","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/2110.01193/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wC6hiwq6KzncnCtYcz3gBfkezWwboPsuQQQrVpF8cKBBO+w62dlxGmOpD+MCE8G/v8ssRPf6L8n3thA0BidODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:17:36.978070Z"},"content_sha256":"d72aa21cdf9ce4c381a036c38c4de326a6b2660037e04242c42f1aa0632f2028","schema_version":"1.0","event_id":"sha256:d72aa21cdf9ce4c381a036c38c4de326a6b2660037e04242c42f1aa0632f2028"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OEU6RT7OOWQBOW3YOTE3FNARXW/bundle.json","state_url":"https://pith.science/pith/OEU6RT7OOWQBOW3YOTE3FNARXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OEU6RT7OOWQBOW3YOTE3FNARXW/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":"2026-07-05T11:17:36Z","links":{"resolver":"https://pith.science/pith/OEU6RT7OOWQBOW3YOTE3FNARXW","bundle":"https://pith.science/pith/OEU6RT7OOWQBOW3YOTE3FNARXW/bundle.json","state":"https://pith.science/pith/OEU6RT7OOWQBOW3YOTE3FNARXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OEU6RT7OOWQBOW3YOTE3FNARXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OEU6RT7OOWQBOW3YOTE3FNARXW","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":"45725333b06b001693bdcb01735221e4895c8f6ba5e39da0e1816ea10a6b9651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-10-04T05:23:27Z","title_canon_sha256":"e3a6d757bc322fd5d5350bc7f1b39bed1b26249030e659372d72f88874d981df"},"schema_version":"1.0","source":{"id":"2110.01193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.01193","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"2110.01193v1","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.01193","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"OEU6RT7OOWQB","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"OEU6RT7OOWQBOW3Y","created_at":"2026-07-05T03:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"OEU6RT7O","created_at":"2026-07-05T03:19:52Z"}],"graph_snapshots":[{"event_id":"sha256:d72aa21cdf9ce4c381a036c38c4de326a6b2660037e04242c42f1aa0632f2028","target":"graph","created_at":"2026-07-05T03:19:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.01193/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $t\\in(0,\\infty)$, $p\\in(1,\\infty)$, $q\\in[1,\\infty]$, $w\\in A_p$ and $v\\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical operators in harmonic analysis, such as the Hardy--Littlewood maximal operator, the Calder\\'on--Zygmund operator, the Riesz potential, singular integral operators with the rough kernel, the Marcinkiewicz integral, the Bochner-Riesz operator, the Littlewood-Paley $g$ function and the intrinsic square function, are considered. Our main method is extrapolation. We obt","authors_text":"Jiang Zhou, Songbai Wang, Yuan Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-10-04T05:23:27Z","title":"Boundedness of some operators on weighted amalgam spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.01193","kind":"arxiv","version":1},"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:b3d21ba11582f4116da91e069e97b00bc195af0fa39973deb85c65f548fb0506","target":"record","created_at":"2026-07-05T03:19:52Z","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":"45725333b06b001693bdcb01735221e4895c8f6ba5e39da0e1816ea10a6b9651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-10-04T05:23:27Z","title_canon_sha256":"e3a6d757bc322fd5d5350bc7f1b39bed1b26249030e659372d72f88874d981df"},"schema_version":"1.0","source":{"id":"2110.01193","kind":"arxiv","version":1}},"canonical_sha256":"7129e8cfee75a0175b7874c9b2b411bdbea7540246328a99aa88c303ab381ee9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7129e8cfee75a0175b7874c9b2b411bdbea7540246328a99aa88c303ab381ee9","first_computed_at":"2026-07-05T03:19:52.804794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:19:52.804794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFmWwCjoOg01mOohWwpWk7QYsZETmaR0Yhh6m+pZnhlmTFb1IgiqYiPJV7+Rmn4WcMNWnmaRI28Z0VrBAQxwBA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:19:52.805149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.01193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3d21ba11582f4116da91e069e97b00bc195af0fa39973deb85c65f548fb0506","sha256:d72aa21cdf9ce4c381a036c38c4de326a6b2660037e04242c42f1aa0632f2028"],"state_sha256":"444c3f3d9ff0a81a755df453fd99cdd8d217bae3c6b8cdeb3730ac6d3d9e65e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dcchrymia7Q5Faui0usdo+7sDIYYYsuP2xhC3vInhVCGUUK1K/E3YRghyqLpM/zvyfNmskdYsYGG+57Tq+K9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T11:17:36.979901Z","bundle_sha256":"c4cd3bbb25982c99a8a8b79670c12051494098a5d5c3e9086ce692b73e4bbc4f"}}