Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems

@article{Lundholm2015FractionalHA,
  title={Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems},
  author={Douglas Lundholm and Phan Th{\`a}nh Nam and Fabian Portmann},
  journal={Archive for Rational Mechanics and Analysis},
  year={2015},
  volume={219},
  pages={1343-1382}
}
We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases. 

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