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Sharp Hardy Identities and Inequalities on Carnot Groups
- Source :
- Advanced Nonlinear Studies. 21:281-302
- Publication Year :
- 2021
- Publisher :
- Walter de Gruyter GmbH, 2021.
-
Abstract
- In this paper we establish general weighted Hardy identities for several subelliptic settings including Hardy identities on the Heisenberg group, Carnot groups with respect to a homogeneous gauge and Carnot–Carathéodory metric, general nilpotent groups, and certain families of Hörmander vector fields. We also introduce new weighted uncertainty principles in these settings. This is done by continuing the program initiated by [N. Lam, G. Lu and L. Zhang, Factorizations and Hardy’s-type identities and inequalities on upper half spaces, Calc. Var. Partial Differential Equations 58 2019, 6, Paper No. 183; N. Lam, G. Lu and L. Zhang, Geometric Hardy’s inequalities with general distance functions, J. Funct. Anal. 279 2020, 8, Article ID 108673] of using the Bessel pairs introduced by [N. Ghoussoub and A. Moradifam, Functional Inequalities: New Perspectives and New Applications, Math. Surveys Monogr. 187, American Mathematical Society, Providence, 2013] to obtain Hardy identities. Using these identities, we are able to improve significantly existing Hardy inequalities in the literature in the aforementioned subelliptic settings. In particular, we establish the Hardy identities and inequalities in the spirit of [H. Brezis and J. L. Vázquez, Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Complut. Madrid 10 1997, 443–469] and [H. Brezis and M. Marcus, Hardy’s inequalities revisited. Dedicated to Ennio De Giorgi, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 25 1997, 1–2, 217–237] in these settings.
- Subjects :
- Pure mathematics
Inequality
General Mathematics
media_common.quotation_subject
010102 general mathematics
Statistical and Nonlinear Physics
01 natural sciences
03 medical and health sciences
symbols.namesake
0302 clinical medicine
symbols
030212 general & internal medicine
0101 mathematics
Carnot cycle
Mathematics
media_common
Subjects
Details
- ISSN :
- 21690375 and 15361365
- Volume :
- 21
- Database :
- OpenAIRE
- Journal :
- Advanced Nonlinear Studies
- Accession number :
- edsair.doi...........f7b8cb188987e256c09795fabe89947a