{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DXMB27YQZDYJIYEH5NP3W2XDMN","short_pith_number":"pith:DXMB27YQ","schema_version":"1.0","canonical_sha256":"1dd81d7f10c8f0946087eb5fbb6ae36375e14ea1f13ca0875631481211372ccb","source":{"kind":"arxiv","id":"1505.03494","version":1},"attestation_state":"computed","paper":{"title":"On the pointwise convergence to initial data of heat and Poisson problems for the Bessel operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Isolda Cardoso","submitted_at":"2015-05-13T18:48:49Z","abstract_excerpt":"We find optimal integrability conditions on the initial data $f$ for the existence of solutions $e^{-t\\Delta_{\\lambda}}f(x)$ and $e^{-t\\sqrt{\\Delta_{\\lambda}}}f(x)$ of the heat and Poisson initial data problems for the Bessel operator $\\Delta_{\\lambda}$ in $\\mathbb{R}^{+}$. We also characterize the most general class of weights $v$ for which the solutions converge a.e. to $f$ for every $f\\in L^{p}(v)$, with $1\\le p<\\infty$. Finally, we show that for such weights and $1<p<\\infty$ the local maximal operators are bounded from $L^{p}(v)$ to $L^{p}(u)$, for some weight $u$."},"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":"1505.03494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-13T18:48:49Z","cross_cats_sorted":[],"title_canon_sha256":"d76fb5fd9465e9b2f67e6286ffe0a3be319c4439999bce25bfb5e8216412b147","abstract_canon_sha256":"d2b45016beacdcf65a9d4e00b2260b676857434e42efdf94327c435bf48c8313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:01.163669Z","signature_b64":"syWUBH57f0jq7gIjLTdnk10+1PLNH3+noeQ7iP/zZJex0Hg1e7GkRY4F9EGiYhECVSRgOHOm1blQF/2c7AM/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dd81d7f10c8f0946087eb5fbb6ae36375e14ea1f13ca0875631481211372ccb","last_reissued_at":"2026-05-18T02:12:01.162957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:01.162957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the pointwise convergence to initial data of heat and Poisson problems for the Bessel operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Isolda Cardoso","submitted_at":"2015-05-13T18:48:49Z","abstract_excerpt":"We find optimal integrability conditions on the initial data $f$ for the existence of solutions $e^{-t\\Delta_{\\lambda}}f(x)$ and $e^{-t\\sqrt{\\Delta_{\\lambda}}}f(x)$ of the heat and Poisson initial data problems for the Bessel operator $\\Delta_{\\lambda}$ in $\\mathbb{R}^{+}$. We also characterize the most general class of weights $v$ for which the solutions converge a.e. to $f$ for every $f\\in L^{p}(v)$, with $1\\le p<\\infty$. Finally, we show that for such weights and $1<p<\\infty$ the local maximal operators are bounded from $L^{p}(v)$ to $L^{p}(u)$, for some weight $u$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03494","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":""},"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":"1505.03494","created_at":"2026-05-18T02:12:01.163058+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03494v1","created_at":"2026-05-18T02:12:01.163058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03494","created_at":"2026-05-18T02:12:01.163058+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXMB27YQZDYJ","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXMB27YQZDYJIYEH","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXMB27YQ","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN","json":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN.json","graph_json":"https://pith.science/api/pith-number/DXMB27YQZDYJIYEH5NP3W2XDMN/graph.json","events_json":"https://pith.science/api/pith-number/DXMB27YQZDYJIYEH5NP3W2XDMN/events.json","paper":"https://pith.science/paper/DXMB27YQ"},"agent_actions":{"view_html":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN","download_json":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN.json","view_paper":"https://pith.science/paper/DXMB27YQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03494&json=true","fetch_graph":"https://pith.science/api/pith-number/DXMB27YQZDYJIYEH5NP3W2XDMN/graph.json","fetch_events":"https://pith.science/api/pith-number/DXMB27YQZDYJIYEH5NP3W2XDMN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN/action/storage_attestation","attest_author":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN/action/author_attestation","sign_citation":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN/action/citation_signature","submit_replication":"https://pith.science/pith/DXMB27YQZDYJIYEH5NP3W2XDMN/action/replication_record"}},"created_at":"2026-05-18T02:12:01.163058+00:00","updated_at":"2026-05-18T02:12:01.163058+00:00"}