Persistence of Rademacher-type and Sobolev-to-Lipschitz properties
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909805400031232 |
|---|---|
| author | Schiavo, Lorenzo Dello Suzuki, Kohei |
| author_facet | Schiavo, Lorenzo Dello Suzuki, Kohei |
| contents | We consider the Rademacher- and Sobolev-to-Lipschitz-type properties for arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the persistence of these properties under localization, globalization, transfer to weighted spaces, tensorization, and direct integration. As byproducts we obtain: necessary and sufficient conditions to identify a quasi-regular strongly local Dirichlet form on an extended metric topological $σ$-finite possibly non-Radon measure space with the Cheeger energy of the space; the tensorization of intrinsic distances; the tensorization of the Varadhan short-time asymptotics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10733 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Persistence of Rademacher-type and Sobolev-to-Lipschitz properties Schiavo, Lorenzo Dello Suzuki, Kohei Metric Geometry Functional Analysis 31C25 (Primary) 30L99, 31E05 (Secondary) We consider the Rademacher- and Sobolev-to-Lipschitz-type properties for arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the persistence of these properties under localization, globalization, transfer to weighted spaces, tensorization, and direct integration. As byproducts we obtain: necessary and sufficient conditions to identify a quasi-regular strongly local Dirichlet form on an extended metric topological $σ$-finite possibly non-Radon measure space with the Cheeger energy of the space; the tensorization of intrinsic distances; the tensorization of the Varadhan short-time asymptotics. |
| title | Persistence of Rademacher-type and Sobolev-to-Lipschitz properties |
| topic | Metric Geometry Functional Analysis 31C25 (Primary) 30L99, 31E05 (Secondary) |
| url | https://arxiv.org/abs/2309.10733 |