Stability of Hölder regularity and weighted functional inequalities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913713070538752 |
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| author | Cho, Soobin Kim, Panki |
| author_facet | Cho, Soobin Kim, Panki |
| contents | We study symmetric Dirichlet forms on metric measure spaces, which may possess both strongly local and pure-jump parts. We introduce a new formulation of a tail condition for jump measures and weighted functional inequalities. Our framework accommodates Dirichlet forms with singular jump measures and those associated with trace processes of mixed-type stable processes. Using these new weighted functional inequalities, we establish stable, equivalent characterizations of Hölder regularity for caloric and harmonic functions. As an application of our main result, we prove the Hölder continuity of caloric functions for a large class of symmetric Markov processes exhibiting boundary blow-up behavior, among other results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Hölder regularity and weighted functional inequalities Cho, Soobin Kim, Panki Probability Analysis of PDEs Primary 60J45, 60J46, 60J76, Secondary 35K08 We study symmetric Dirichlet forms on metric measure spaces, which may possess both strongly local and pure-jump parts. We introduce a new formulation of a tail condition for jump measures and weighted functional inequalities. Our framework accommodates Dirichlet forms with singular jump measures and those associated with trace processes of mixed-type stable processes. Using these new weighted functional inequalities, we establish stable, equivalent characterizations of Hölder regularity for caloric and harmonic functions. As an application of our main result, we prove the Hölder continuity of caloric functions for a large class of symmetric Markov processes exhibiting boundary blow-up behavior, among other results. |
| title | Stability of Hölder regularity and weighted functional inequalities |
| topic | Probability Analysis of PDEs Primary 60J45, 60J46, 60J76, Secondary 35K08 |
| url | https://arxiv.org/abs/2503.00318 |