{"paper":{"title":"Fractional heat semigroups on metric measure spaces with finite densities and applications to fractional dissipative equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jizheng Huang, Pengtao Li, Shaoguang Shi, Yu Liu","submitted_at":"2019-08-21T14:33:35Z","abstract_excerpt":"Let $(\\mathbb M, d,\\mu)$ be a metric measure space with upper and lower\n  densities: $$ \\begin{cases} |||\\mu|||_{\\beta}:=\\sup_{(x,r)\\in \\mathbb M\\times(0,\\infty)} \\mu(B(x,r))r^{-\\beta}<\\infty;\\\\ |||\\mu|||_{\\beta^{\\star}}:=\\inf_{(x,r)\\in \\mathbb M\\times(0,\\infty)} \\mu(B(x,r))r^{-\\beta^{\\star}}>0, \\end{cases} $$ where $\\beta, \\beta^{\\star}$ are two positive constants which are less than or equal to the Hausdorff dimension of $\\mathbb M$. Assume that $p_t(\\cdot,\\cdot)$ is a heat kernel on $\\mathbb M$ satisfying Gaussian upper estimates and $\\mathcal L$ is the generator of the semigroup associated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07895","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/1908.07895/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"}