- 11-6 A.A. Balinsky, W.D. Evans and T. Umeda
- The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$
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Jan 17, 11
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Abstract. Dirac-Sobolev and Dirac-Hardy inequalities in
$L^1$ are established in which the $L^p$ spaces which feature in
the classical Sobolev and Hardy inequalities are replaced by weak
$L^p$ spaces. Counter examples to the analogues of the classical
inequalities are shown to be provided by zero modes for
appropriate Pauli operators constructed by Loss and Yau.
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