An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908579485712384 |
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| author | Anttila, Riku |
| author_facet | Anttila, Riku |
| contents | In this work, we establish a new characterization of sub-Gaussian heat kernel estimates for strongly local regular Dirichlet forms on metric measure spaces. Our formulation is based on the newly introduced cutoff energy condition, which offers a simpler and more transparent alternative for earlier technical energy inequalities, in particular the cutoff Sobolev inequality. The main idea of our approach is to reinterpret the cutoff Sobolev inequality as a Poincaré type inequality, and analyze it using Hajłasz--Koskela techniques from analysis on metric spaces. Applications of the new characterization are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces Anttila, Riku Probability Functional Analysis 31C25, 30L99, 35K08, 31E05, 46E36 In this work, we establish a new characterization of sub-Gaussian heat kernel estimates for strongly local regular Dirichlet forms on metric measure spaces. Our formulation is based on the newly introduced cutoff energy condition, which offers a simpler and more transparent alternative for earlier technical energy inequalities, in particular the cutoff Sobolev inequality. The main idea of our approach is to reinterpret the cutoff Sobolev inequality as a Poincaré type inequality, and analyze it using Hajłasz--Koskela techniques from analysis on metric spaces. Applications of the new characterization are also discussed. |
| title | An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces |
| topic | Probability Functional Analysis 31C25, 30L99, 35K08, 31E05, 46E36 |
| url | https://arxiv.org/abs/2509.04155 |