Hardy type inequalities for the fractional relativistic operator
We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of th...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-05-01
|
| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2022018?viewType=HTML |
| _version_ | 1818205989143314432 |
|---|---|
| author | Luz Roncal |
| author_facet | Luz Roncal |
| author_sort | Luz Roncal |
| collection | DOAJ |
| description | We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of the ground state representation in the spirit of Frank, Lieb, and Seiringer. |
| first_indexed | 2024-12-12T04:05:53Z |
| format | Article |
| id | doaj.art-3651d67dbc1148029795c3d9532aa51c |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-12T04:05:53Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-3651d67dbc1148029795c3d9532aa51c2022-12-22T00:38:46ZengAIMS PressMathematics in Engineering2640-35012022-05-014311610.3934/mine.2022018Hardy type inequalities for the fractional relativistic operatorLuz Roncal 01. BCAM - Basque Center for Applied Mathematics 48009 Bilbao, Spain 2. Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain 3. Universidad del País Vasco/Euskal Herriko Unibertsitatea, 48080 Bilbao, SpainWe prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of the ground state representation in the spirit of Frank, Lieb, and Seiringer.https://www.aimspress.com/article/doi/10.3934/mine.2022018?viewType=HTMLtrace hardy inequalityhardy inequalityextension problemground state representationfractional operator |
| spellingShingle | Luz Roncal Hardy type inequalities for the fractional relativistic operator Mathematics in Engineering trace hardy inequality hardy inequality extension problem ground state representation fractional operator |
| title | Hardy type inequalities for the fractional relativistic operator |
| title_full | Hardy type inequalities for the fractional relativistic operator |
| title_fullStr | Hardy type inequalities for the fractional relativistic operator |
| title_full_unstemmed | Hardy type inequalities for the fractional relativistic operator |
| title_short | Hardy type inequalities for the fractional relativistic operator |
| title_sort | hardy type inequalities for the fractional relativistic operator |
| topic | trace hardy inequality hardy inequality extension problem ground state representation fractional operator |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2022018?viewType=HTML |
| work_keys_str_mv | AT luzroncal hardytypeinequalitiesforthefractionalrelativisticoperator |