{"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 $M\\times M$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07650","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/1908.07650/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"}