Optimal upper bounds are proved for the electron density of non-interacting relativistic atoms described by Chandrasekhar and Dirac operators.
Frank , Konstantin Merz , Heinz Siedentop , and Barry Simon
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Equivalence of homogeneous L^p-Sobolev norms for Hardy operators with and without potential is established via new square function estimates for slowly decaying heat kernels.
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Sharp upper bounds for the density of relativistic atoms: Noninteracting case
Optimal upper bounds are proved for the electron density of non-interacting relativistic atoms described by Chandrasekhar and Dirac operators.
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Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space
Equivalence of homogeneous L^p-Sobolev norms for Hardy operators with and without potential is established via new square function estimates for slowly decaying heat kernels.