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

2003/09/30 by J. Dolbeault, Dolbeault, J., M. J. Esteban +5
Mathematics · Physics and Astronomy · #35Q40 #35Q75 #46N50 #81Q10 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35Q40 #msc:35Q75 #msc:46N50 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math-ph/0309065

LaTex, 22 pages

arxiv created 2003/09/30 · arxiv updated 2009/12/01

Abstract

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.

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