Functional inequalities on Lie groups and applications
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Date
2023
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Faculty of Engineering and Natural Sciences
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.
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Keywords
apps, Preliminaries, Functional inequalities
Citation
Kalaman M / Functional inequalities on Lie groups and applications / 7M05401 - Department of Mathematics and Natural Sciences / 2023