Hardy-type estimates for Dirac operators

Dolbeault, Jean; Duoandikoetxea, Javier; Esteban, Maria J.; Vega, Luis

Dolbeault, Jean; Duoandikoetxea, Javier; Esteban, Maria J.; Vega, Luis (2007), Hardy-type estimates for Dirac operators, Annales Scientifiques de l'École Normale Supérieure, 40, 6, p. 885-900

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00112858/en/

Date

2007

Journal name

Annales Scientifiques de l'École Normale Supérieure

Volume

Number

Pages

885-900

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Author(s)

Dolbeault, Jean

Duoandikoetxea, Javier
Esteban, Maria J.

Vega, Luis

Abstract (EN)

We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator.

Subjects / Keywords

Hardy inequality; Dirac operator; Coulomb potential; Optimal constants; Dirac-Coulomb Hamiltonian; relativistic Hydrogen atom