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Under general volume doubling condition on $(M,d,\\mu)$ and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp.\\ two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev ineq"},"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":"1908.07650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-20T23:54:55Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"7243be9dbf909578ee03c4f4e75801e363e9cd4529f8a68f8c5d8d14b0a2de2a","abstract_canon_sha256":"e71c5cf7c37e74f9da0ee0aa310281deb547ab10e7f22c999e68e94ce5fbae01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:59.937966Z","signature_b64":"LIvYqDveSlFOhdtZbHp6ZdvNcfo31EV+bi8crkVkcBBitK1aP64vp0bTLhSt4GfvHsS7dbDR7c0fjH4DJ2xxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"419edbca55cd2ae2ccaabbd8cf85f4f51431759701462e2dd25e0d4bfe7a4e45","last_reissued_at":"2026-07-04T23:58:59.937603Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:59.937603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Jian Wang, Takashi Kumagai, Zhen-Qing Chen","submitted_at":"2019-08-20T23:54:55Z","abstract_excerpt":"In this paper, we consider the following symmetric Dirichlet forms on a metric measure space $(M,d,\\mu)$: $$\\mathcal{E}(f,g) = \\mathcal{E}(^{(c)}(f,g)+\\int_{M\\times M} (f(x)-f(y))(g(x)-g(y))\\,J(dx,dy),$$ where $\\mathcal{E}(^{(c)}$ is a strongly local symmetric bilinear form and $J(dx,dy)$ is a symmetric Random measure on $M\\times M$. 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