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

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• 作者：Dolbeault ; Jean ; Esteban ; Maria J. ; Loss ; Michael ; Vega ; Luis
• 关键词：primary 35Q40 ; 35Q75 ; 46N50 ; 81Q10 ; secondary 34L40 ; 35P05 ; 47A05 ; 47F05 ; 47N50 ; 81V45 ; 81V55 ; Hardy inequality ; Dirac operator ; Optimal constants ; Dirac&ndash ; Coulomb Hamiltonian ; Relativistic Hydrogen atom
• 刊名：Journal of Functional Analysis
• 出版年：2004
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：November 1, 2004
• 卷：216
• 期：1
• 页码：1-21
• 文件大小：307 K

摘要

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.