Functional inequalities on Lie groups and applications
| dc.contributor.author | Kalaman M. | |
| dc.date.accessioned | 2025-06-12T04:30:21Z | |
| dc.date.available | 2025-06-12T04:30:21Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | In this thesis we discuss sharp remainder formulae for the cylindrical extensions of the improved Hardy inequalities. For more general p we obtain cylindrical improved L?-Hardy identities for all real-valued functions f € Cg°(R"\{2x' = 0}), while in L? case we have them for any complex-valued function f € Cg°(R"\{z' = 0}). Moreover, we show cylindrical L?-Hardy inequalities for all complex-valued functions f € Cp°(IR"\{a’ = 0}). As applications, we establish Heisenberg-PaulWeyl type uncertainty principles and Caffarelli-Kohn-Nirenberg type inequalities. In particular cases, these inequalities imply new functional inequalities, which are not covered by the classical Caffarelli-Kohn-Nirenberg inequalities. Furthermore, the thesis contains L* and L? identities with logarithmic type functions on the quasi-ball B(0,R) with R > 0. In addition, we also discuss the results in the setting of homogeneous Lie groups. | |
| dc.identifier.citation | Kalaman M / Functional inequalities on Lie groups and applications / 7M05401 - Department of Mathematics and Natural Sciences / 2023 | |
| dc.identifier.uri | https://repository.sdu.edu.kz/handle/123456789/1756 | |
| dc.language.iso | en | |
| dc.publisher | Faculty of Engineering and Natural Sciences | |
| dc.subject | apps | |
| dc.subject | Preliminaries | |
| dc.subject | Functional inequalities | |
| dc.title | Functional inequalities on Lie groups and applications | |
| dc.type | Thesis |