The Poincaré Inequality Does Not Improve with Blow-Up
For each β > 1 we construct a family Fβ of metric measure spaces which is closed under the operation of taking weak-tangents (i.e. blow-ups), and such that each element of Fβ admits a (1, P)-Poincaré inequality if and only if P > β.
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-12-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2016-0018 |
| _version_ | 1818362863623864320 |
|---|---|
| author | Schioppa Andrea |
| author_facet | Schioppa Andrea |
| author_sort | Schioppa Andrea |
| collection | DOAJ |
| description | For each β > 1 we construct a family Fβ of metric measure spaces which is closed under the operation
of taking weak-tangents (i.e. blow-ups), and such that each element of Fβ admits a (1, P)-Poincaré
inequality if and only if P > β. |
| first_indexed | 2024-12-13T21:39:20Z |
| format | Article |
| id | doaj.art-18449532c81f4cfc90bc9e936dbf2d5f |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-13T21:39:20Z |
| publishDate | 2016-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-18449532c81f4cfc90bc9e936dbf2d5f2022-12-21T23:30:36ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742016-12-014110.1515/agms-2016-0018agms-2016-0018The Poincaré Inequality Does Not Improve with Blow-UpSchioppa Andrea0Swiss Federal Institute of Technology in Zurich (ETHZ) ZürichFor each β > 1 we construct a family Fβ of metric measure spaces which is closed under the operation of taking weak-tangents (i.e. blow-ups), and such that each element of Fβ admits a (1, P)-Poincaré inequality if and only if P > β.https://doi.org/10.1515/agms-2016-0018poincaré inequality modulus |
| spellingShingle | Schioppa Andrea The Poincaré Inequality Does Not Improve with Blow-Up Analysis and Geometry in Metric Spaces poincaré inequality modulus |
| title | The Poincaré Inequality Does Not Improve with Blow-Up |
| title_full | The Poincaré Inequality Does Not Improve with Blow-Up |
| title_fullStr | The Poincaré Inequality Does Not Improve with Blow-Up |
| title_full_unstemmed | The Poincaré Inequality Does Not Improve with Blow-Up |
| title_short | The Poincaré Inequality Does Not Improve with Blow-Up |
| title_sort | poincare inequality does not improve with blow up |
| topic | poincaré inequality modulus |
| url | https://doi.org/10.1515/agms-2016-0018 |
| work_keys_str_mv | AT schioppaandrea thepoincareinequalitydoesnotimprovewithblowup AT schioppaandrea poincareinequalitydoesnotimprovewithblowup |