Further study on domains and quasihyperbolic distances
Abstract We establish constructive geometric tools for determining when a domain is L s $L^{s}$ -averaging and obtain upper and lower bounds for the L s $L^{s}$ -integrals of the quasihyperbolic distance. We also construct examples that are helpful to understand our geometric tools and the relations...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02882-1 |
| _version_ | 1798018166651092992 |
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| author | Shusen Ding Dylan Helliwell Gavin Pandya Arya Yae |
| author_facet | Shusen Ding Dylan Helliwell Gavin Pandya Arya Yae |
| author_sort | Shusen Ding |
| collection | DOAJ |
| description | Abstract We establish constructive geometric tools for determining when a domain is L s $L^{s}$ -averaging and obtain upper and lower bounds for the L s $L^{s}$ -integrals of the quasihyperbolic distance. We also construct examples that are helpful to understand our geometric tools and the relationship between p-Poincaré domains and L s $L^{s}$ -averaging domains. Finally, finite unions of L s ( μ ) $L^{s}(\mu )$ -averaging domains are explored. |
| first_indexed | 2024-04-11T16:19:24Z |
| format | Article |
| id | doaj.art-0286349ed3e440a08776a866c78a928f |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-11T16:19:24Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-0286349ed3e440a08776a866c78a928f2022-12-22T04:14:25ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-11-012022112310.1186/s13660-022-02882-1Further study on domains and quasihyperbolic distancesShusen Ding0Dylan Helliwell1Gavin Pandya2Arya Yae3Mathematics Department, Seattle UniversityMathematics Department, Seattle UniversityMathematics Department, Seattle UniversityMathematics Department, Seattle UniversityAbstract We establish constructive geometric tools for determining when a domain is L s $L^{s}$ -averaging and obtain upper and lower bounds for the L s $L^{s}$ -integrals of the quasihyperbolic distance. We also construct examples that are helpful to understand our geometric tools and the relationship between p-Poincaré domains and L s $L^{s}$ -averaging domains. Finally, finite unions of L s ( μ ) $L^{s}(\mu )$ -averaging domains are explored.https://doi.org/10.1186/s13660-022-02882-1Poincaré domainL s $L^{s}$ -averaging domainQuasihyperbolic distanceWhitney subdivision |
| spellingShingle | Shusen Ding Dylan Helliwell Gavin Pandya Arya Yae Further study on domains and quasihyperbolic distances Journal of Inequalities and Applications Poincaré domain L s $L^{s}$ -averaging domain Quasihyperbolic distance Whitney subdivision |
| title | Further study on domains and quasihyperbolic distances |
| title_full | Further study on domains and quasihyperbolic distances |
| title_fullStr | Further study on domains and quasihyperbolic distances |
| title_full_unstemmed | Further study on domains and quasihyperbolic distances |
| title_short | Further study on domains and quasihyperbolic distances |
| title_sort | further study on domains and quasihyperbolic distances |
| topic | Poincaré domain L s $L^{s}$ -averaging domain Quasihyperbolic distance Whitney subdivision |
| url | https://doi.org/10.1186/s13660-022-02882-1 |
| work_keys_str_mv | AT shusending furtherstudyondomainsandquasihyperbolicdistances AT dylanhelliwell furtherstudyondomainsandquasihyperbolicdistances AT gavinpandya furtherstudyondomainsandquasihyperbolicdistances AT aryayae furtherstudyondomainsandquasihyperbolicdistances |