The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$

Details The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$ The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$

2011-01-17

arxiv.org/abs/1101.3129v1

Mathematics

Spectral Theory

11 pages. To appear in Publ. RIMS, Kyoto University

Scientific paper

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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