{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:CANDUTO2LQZ77TYJB46WVU7CV7","short_pith_number":"pith:CANDUTO2","schema_version":"1.0","canonical_sha256":"101a3a4dda5c33ffcf090f3d6ad3e2afc6cf2245eb0d7795910a084070f26b71","source":{"kind":"arxiv","id":"2310.08458","version":1},"attestation_state":"computed","paper":{"title":"Discrete Riesz Potentials on Discrete Weighted Morrey Spaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Baode Li, Shuai Yang, Xuebing Hao","submitted_at":"2023-10-12T16:18:20Z","abstract_excerpt":"Let $0<\\alpha<1$. We obtain the boundedness of the discrete fractional Hardy-Littlewood maximal operators ${\\mathcal M}_\\alpha$ on discrete weighted Lebesgue spaces. From this and a discrete version of Whitney decomposition theorem, we deduce the boundedness of the discrete Riesz potentials $I_\\alpha$ on discrete weighted Lebesgue spaces. The boundedness of $I_\\alpha$ on discrete weighted Morrey spaces is further obtained. Moreover, the boundedness of ${\\mathcal M}_\\alpha$ is also obtained which is new even for unweighted case."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.08458","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2023-10-12T16:18:20Z","cross_cats_sorted":[],"title_canon_sha256":"d46ad07ff8e07db806ebbbf2c5a08ba85742831b8a51bf80ba636974e4e7415b","abstract_canon_sha256":"f7e93c58945e08b5833a23c9c259eea5aaebc9298d42ce986a617ce0396b00e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:00:15.862614Z","signature_b64":"Asdyfx3f+8SRcYiKHVWDPfWt9tdSppdtinGCErChXEB//7voPDEp0ie6igB1GU/uou4ER1Ms9rE6EiyfAH0YDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"101a3a4dda5c33ffcf090f3d6ad3e2afc6cf2245eb0d7795910a084070f26b71","last_reissued_at":"2026-07-05T07:00:15.862133Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:00:15.862133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete Riesz Potentials on Discrete Weighted Morrey Spaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Baode Li, Shuai Yang, Xuebing Hao","submitted_at":"2023-10-12T16:18:20Z","abstract_excerpt":"Let $0<\\alpha<1$. We obtain the boundedness of the discrete fractional Hardy-Littlewood maximal operators ${\\mathcal M}_\\alpha$ on discrete weighted Lebesgue spaces. From this and a discrete version of Whitney decomposition theorem, we deduce the boundedness of the discrete Riesz potentials $I_\\alpha$ on discrete weighted Lebesgue spaces. The boundedness of $I_\\alpha$ on discrete weighted Morrey spaces is further obtained. Moreover, the boundedness of ${\\mathcal M}_\\alpha$ is also obtained which is new even for unweighted case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.08458","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/2310.08458/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2310.08458","created_at":"2026-07-05T07:00:15.862191+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.08458v1","created_at":"2026-07-05T07:00:15.862191+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.08458","created_at":"2026-07-05T07:00:15.862191+00:00"},{"alias_kind":"pith_short_12","alias_value":"CANDUTO2LQZ7","created_at":"2026-07-05T07:00:15.862191+00:00"},{"alias_kind":"pith_short_16","alias_value":"CANDUTO2LQZ77TYJ","created_at":"2026-07-05T07:00:15.862191+00:00"},{"alias_kind":"pith_short_8","alias_value":"CANDUTO2","created_at":"2026-07-05T07:00:15.862191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.18858","citing_title":"Why you shouldn't fully trust ChatGPT: A synthesis of this AI tool's error rates across disciplines and the software engineering lifecycle","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7","json":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7.json","graph_json":"https://pith.science/api/pith-number/CANDUTO2LQZ77TYJB46WVU7CV7/graph.json","events_json":"https://pith.science/api/pith-number/CANDUTO2LQZ77TYJB46WVU7CV7/events.json","paper":"https://pith.science/paper/CANDUTO2"},"agent_actions":{"view_html":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7","download_json":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7.json","view_paper":"https://pith.science/paper/CANDUTO2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.08458&json=true","fetch_graph":"https://pith.science/api/pith-number/CANDUTO2LQZ77TYJB46WVU7CV7/graph.json","fetch_events":"https://pith.science/api/pith-number/CANDUTO2LQZ77TYJB46WVU7CV7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7/action/storage_attestation","attest_author":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7/action/author_attestation","sign_citation":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7/action/citation_signature","submit_replication":"https://pith.science/pith/CANDUTO2LQZ77TYJB46WVU7CV7/action/replication_record"}},"created_at":"2026-07-05T07:00:15.862191+00:00","updated_at":"2026-07-05T07:00:15.862191+00:00"}