JournalsprimsVol. 47, No. 3pp. 791–801

The Dirac-Hardy and Dirac-Sobolev inequalities in L1L^1

  • Alexander Balinsky

    University of Wales Cardiff, UK
  • W. Desmond Evans

    University of Wales Cardiff, UK
  • Tomio Umeda

    University of Hyogo, Himeji, Japan
The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$ cover
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Abstract

Dirac-Sobolev and Dirac-Hardy inequalities in L1L^1 are established in which the LpL^p spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak LpL^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.

Cite this article

Alexander Balinsky, W. Desmond Evans, Tomio Umeda, The Dirac-Hardy and Dirac-Sobolev inequalities in L1L^1. Publ. Res. Inst. Math. Sci. 47 (2011), no. 3, pp. 791–801

DOI 10.2977/PRIMS/51