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Journal of the London Mathematical Society Advance Access originally published online on December 10, 2007
Journal of the London Mathematical Society 2008 77(1):99-115; doi:10.1112/jlms/jdm091
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© 2007 London Mathematical Society

Many-particle Hardy inequalities

M. Hoffmann-Ostenhof

Fakultät für Mathematik
Universität Wien
Nordbergstrasse 15
A-1090 Wien
Austria
Maria.Hoffmann-Ostenhof{at}univie.ac.at

T. Hoffmann-Ostenhof

Institut für Theoretische Chemie
Universität Wien
Währinger Strasse 17
A-1090 Wien
Austria
and
International Erwin Schrödinger Institute for Mathematical Physics Boltzmanngasse 9
A-1090 Wien
Austria
thoffman{at}esi.ac.at

A. Laptev

Department of Mathematics
KTH
100 44 Stockholm
Sweden

J. Tidblom

Department of Mathematics
University of Stockholm
106 91 Stockholm
Sweden
jespert{at}math.su.se

In this paper we prove three different types of the so-called many-particle Hardy inequalities. One of them is a ‘classical type’ which is valid in any dimension d != 2. The second type deals with 2-dimensional magnetic Dirichlet forms, where every particle is supplied with a solenoid. Finally we show that Hardy inequalities for fermionic functions (fully anti-symmetric for d = 1, 2) hold true in all dimensions.

2000 Mathematics Subject Classification 35B05.

The authors are grateful for partial support by the ESF European Programme ‘SPECT’. T. Hoffmann–Ostenhof has been partially supported by the Góran Gustafsson Foundation.

Received August 4, 2006; published online December 10, 2007.


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