Stable characterization of diagonal heat kernel upper bounds for symmetric Dirichlet forms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913644785172480 |
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| author | Cho, Soobin |
| author_facet | Cho, Soobin |
| contents | We present a stable characterization of on-diagonal upper bounds for heat kernels associated with regular Dirichlet forms on metric measure spaces satisfying the volume doubling property. Our conditions include integral bounds on the jump kernel outside metric balls, a variant of the Faber-Krahn inequality, a cutoff Sobolev inequality, and an integral control of inverse square volumes of balls with respect to the jump kernel. Crucially, we do not assume that the jump kernel has a density, and we show that these assumptions are essentially optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06866 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable characterization of diagonal heat kernel upper bounds for symmetric Dirichlet forms Cho, Soobin Analysis of PDEs Probability 2020 Mathematics Subject Classification: 35K08, 31C25, 60J35 We present a stable characterization of on-diagonal upper bounds for heat kernels associated with regular Dirichlet forms on metric measure spaces satisfying the volume doubling property. Our conditions include integral bounds on the jump kernel outside metric balls, a variant of the Faber-Krahn inequality, a cutoff Sobolev inequality, and an integral control of inverse square volumes of balls with respect to the jump kernel. Crucially, we do not assume that the jump kernel has a density, and we show that these assumptions are essentially optimal. |
| title | Stable characterization of diagonal heat kernel upper bounds for symmetric Dirichlet forms |
| topic | Analysis of PDEs Probability 2020 Mathematics Subject Classification: 35K08, 31C25, 60J35 |
| url | https://arxiv.org/abs/2501.06866 |