{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KX6MQUIQGA2IY7FXNED7VUQCUT","short_pith_number":"pith:KX6MQUIQ","schema_version":"1.0","canonical_sha256":"55fcc8511030348c7cb76907fad202a4d32575295c549a4d001c2fe7d0c48997","source":{"kind":"arxiv","id":"1703.02152","version":2},"attestation_state":"computed","paper":{"title":"Gradient estimates for heat kernels and harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.DG"],"primary_cat":"math.MG","authors_text":"Adam Sikora, Pekka Koskela, Renjin Jiang, Thierry Coulhon","submitted_at":"2017-03-06T23:53:43Z","abstract_excerpt":"Let $(X,d,\\mu)$ be a doubling metric measure space endowed with a Dirichlet form $\\E$ deriving from a \"carr\\'e du champ\". Assume that $(X,d,\\mu,\\E)$ supports a scale-invariant $L^2$-Poincar\\'e inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\\in (2,\\infty]$:\n  (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat semigroup;\n  (ii) $(RH_p)$: $L^p$-reverse H\\\"older inequality for the gradients of harmonic functions;\n  (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\\infty$);\n  (iv) $(GBE)$: a g"},"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":"1703.02152","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-03-06T23:53:43Z","cross_cats_sorted":["math.AP","math.CA","math.DG"],"title_canon_sha256":"45fa38d3782b75a3b07b90ece5124ed0f4a0387494641e706abce115ec8bddf6","abstract_canon_sha256":"15ca304d3634e5a8f8872a42cfe61c0e85affd4c6b97eb22447871a6cbf92c52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:59.328679Z","signature_b64":"Wx98MeaCutA1ComQ1XpBDNjkiaFPh6yHThvfvrm5WGjOt39Wv3Dq6V7ksJCZ2OLE5dPWwhL2k1lDwbG5MxRnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55fcc8511030348c7cb76907fad202a4d32575295c549a4d001c2fe7d0c48997","last_reissued_at":"2026-05-18T00:33:59.328048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:59.328048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradient estimates for heat kernels and harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.DG"],"primary_cat":"math.MG","authors_text":"Adam Sikora, Pekka Koskela, Renjin Jiang, Thierry Coulhon","submitted_at":"2017-03-06T23:53:43Z","abstract_excerpt":"Let $(X,d,\\mu)$ be a doubling metric measure space endowed with a Dirichlet form $\\E$ deriving from a \"carr\\'e du champ\". Assume that $(X,d,\\mu,\\E)$ supports a scale-invariant $L^2$-Poincar\\'e inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\\in (2,\\infty]$:\n  (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat semigroup;\n  (ii) $(RH_p)$: $L^p$-reverse H\\\"older inequality for the gradients of harmonic functions;\n  (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\\infty$);\n  (iv) $(GBE)$: a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02152","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.02152","created_at":"2026-05-18T00:33:59.328131+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02152v2","created_at":"2026-05-18T00:33:59.328131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02152","created_at":"2026-05-18T00:33:59.328131+00:00"},{"alias_kind":"pith_short_12","alias_value":"KX6MQUIQGA2I","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KX6MQUIQGA2IY7FX","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KX6MQUIQ","created_at":"2026-05-18T12:31:28.150371+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/KX6MQUIQGA2IY7FXNED7VUQCUT","json":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT.json","graph_json":"https://pith.science/api/pith-number/KX6MQUIQGA2IY7FXNED7VUQCUT/graph.json","events_json":"https://pith.science/api/pith-number/KX6MQUIQGA2IY7FXNED7VUQCUT/events.json","paper":"https://pith.science/paper/KX6MQUIQ"},"agent_actions":{"view_html":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT","download_json":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT.json","view_paper":"https://pith.science/paper/KX6MQUIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02152&json=true","fetch_graph":"https://pith.science/api/pith-number/KX6MQUIQGA2IY7FXNED7VUQCUT/graph.json","fetch_events":"https://pith.science/api/pith-number/KX6MQUIQGA2IY7FXNED7VUQCUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT/action/storage_attestation","attest_author":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT/action/author_attestation","sign_citation":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT/action/citation_signature","submit_replication":"https://pith.science/pith/KX6MQUIQGA2IY7FXNED7VUQCUT/action/replication_record"}},"created_at":"2026-05-18T00:33:59.328131+00:00","updated_at":"2026-05-18T00:33:59.328131+00:00"}