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An analytical proof of Hardy-like inequalities related to the Dirac operator

Loss, Michael; Esteban, Maria J.; Dolbeault, Jean; Vega, Luis (2004), An analytical proof of Hardy-like inequalities related to the Dirac operator, Journal of Functional Analysis, 216, 1, p. 1-21. http://dx.doi.org/10.1016/j.jfa.2003.09.010

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
Journal of Functional Analysis
Volume
216
Number
1
Publisher
Elsevier
Pages
1-21
Publication identifier
Metadata
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Author(s)
Loss, Michael
Esteban, Maria J. cc
Dolbeault, Jean cc
Vega, Luis
Abstract (EN)
We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac–Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.
Subjects / Keywords
Relativistic Hydrogen atom; Dirac–Coulomb Hamiltonian; Optimal constants; Dirac operator; Hardy inequality