Preserving Besov (fractional Sobolev) energies under sphericalization and flattening
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915968462094336 |
|---|---|
| author | Björn, Anders Björn, Jana Korte, Riikka Rogovin, Sari Takala, Timo |
| author_facet | Björn, Anders Björn, Jana Korte, Riikka Rogovin, Sari Takala, Timo |
| contents | We introduce a new sphericalization mapping for metric spaces that is applicable in very general situations, including totally disconnected fractal type sets. For an unbounded complete metric space which is uniformly perfect at a base point for large radii and equipped with a doubling measure, we make a more specific construction based on the measure and equip it with a weighted measure. This mapping is then shown to preserve the doubling property of the measure and the Besov (fractional Sobolev) energy.
The corresponding results for flattening of bounded complete metric spaces are also obtained. Finally, it is shown that for the composition of a sphericalization with a flattening, or vice versa, the obtained space is biLipschitz equivalent with the original space and the resulting measure is comparable to the original measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Preserving Besov (fractional Sobolev) energies under sphericalization and flattening Björn, Anders Björn, Jana Korte, Riikka Rogovin, Sari Takala, Timo Functional Analysis Primary: 30L10 Secondary: 31E05, 46E36 We introduce a new sphericalization mapping for metric spaces that is applicable in very general situations, including totally disconnected fractal type sets. For an unbounded complete metric space which is uniformly perfect at a base point for large radii and equipped with a doubling measure, we make a more specific construction based on the measure and equip it with a weighted measure. This mapping is then shown to preserve the doubling property of the measure and the Besov (fractional Sobolev) energy. The corresponding results for flattening of bounded complete metric spaces are also obtained. Finally, it is shown that for the composition of a sphericalization with a flattening, or vice versa, the obtained space is biLipschitz equivalent with the original space and the resulting measure is comparable to the original measure. |
| title | Preserving Besov (fractional Sobolev) energies under sphericalization and flattening |
| topic | Functional Analysis Primary: 30L10 Secondary: 31E05, 46E36 |
| url | https://arxiv.org/abs/2409.17809 |