Sharp Hardy Identities and Inequalities on Carnot Groups
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.
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Sprache
-
Englisch
- Erschienen in
-
Sharp Hardy Identities and Inequalities on Carnot Groups ; volume:21 ; number:2 ; year:2021 ; pages:281-302 ; extent:22
Advanced nonlinear studies ; 21, Heft 2 (2021), 281-302 (gesamt 22)
- Urheber
-
Flynn, Joshua
Lam, Nguyen
Lu, Guozhen
- DOI
-
10.1515/ans-2021-2123
- URN
-
urn:nbn:de:101:1-2405031629369.791458342164
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
14.08.2025, 11:01 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Flynn, Joshua
- Lam, Nguyen
- Lu, Guozhen
Ähnliche Objekte (12)
Anisotropic Picone identities and anisotropic Hardy inequalities
Sharp Caffarelli–Kohn–Nirenberg-Type Inequalities on Carnot Groups
Some new sharp limit Hardy-type inequalities via convexity
Sharp Exponents for Anisotropic Hardy–Littlewood Type of Inequalities
L p Hardy's identities and inequalities for Dunkl operators
Hardy type inequalities in L p $L^p}$ with sharp remainders
Weighted Hardy and Rellich Types Inequalities on the Heisenberg Group with Sharp Constants
Sharp subcritical and critical L p $L^p}$ Hardy inequalities on the sphere
Discrete Hardy-type Inequalities
Hardy inequalities on graphs
Hardy–Sobolev interpolation inequalities
Sharp Martingale and Semimartingale Inequalities
Anisotropic Picone identities and anisotropic Hardy inequalities
Sharp Caffarelli–Kohn–Nirenberg-Type Inequalities on Carnot Groups
Some new sharp limit Hardy-type inequalities via convexity
Sharp Exponents for Anisotropic Hardy–Littlewood Type of Inequalities
L p Hardy's identities and inequalities for Dunkl operators
Hardy type inequalities in L p $L^p}$ with sharp remainders
Weighted Hardy and Rellich Types Inequalities on the Heisenberg Group with Sharp Constants
Sharp subcritical and critical L p $L^p}$ Hardy inequalities on the sphere
Discrete Hardy-type Inequalities
Hardy inequalities on graphs
Hardy–Sobolev interpolation inequalities
Sharp Martingale and Semimartingale Inequalities
Anisotropic Picone identities and anisotropic Hardy inequalities
Sharp Caffarelli–Kohn–Nirenberg-Type Inequalities on Carnot Groups
Some new sharp limit Hardy-type inequalities via convexity
Sharp Exponents for Anisotropic Hardy–Littlewood Type of Inequalities
L p Hardy's identities and inequalities for Dunkl operators
Hardy type inequalities in L p $L^p}$ with sharp remainders
Weighted Hardy and Rellich Types Inequalities on the Heisenberg Group with Sharp Constants
Sharp subcritical and critical L p $L^p}$ Hardy inequalities on the sphere
Discrete Hardy-type Inequalities
Hardy inequalities on graphs
Hardy–Sobolev interpolation inequalities