---
_id: '1622'
abstract:
- lang: eng
  text: 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.
acknowledgement: "We thank Jan  Philip  Solovej, Robert Seiringer and Vladimir Maz’ya
  for helpful discussions, as well as Rupert Frank\r\nand the anonymous referee for
  useful comments. Part of this work has been carried out during a visit at the Institut
  Mittag-Leffler (Stockholm). D.L. acknowledges financial support by the grant KAW
  2010.0063 from the Knut and Alice Wallenberg Foundation and the Swedish Research
  Council grant no. 2013-4734. P.T.N. is supported by the People Programme (Marie
  Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013)
  under REA grant agreement no. 291734. F.P. acknowledges support from the ERC project
  no. 321029 “The\r\nmathematics of the structure of matter”."
article_processing_charge: No
arxiv: 1
author:
- first_name: Douglas
  full_name: Lundholm, Douglas
  last_name: Lundholm
- first_name: Phan
  full_name: Nam, Phan
  id: 404092F4-F248-11E8-B48F-1D18A9856A87
  last_name: Nam
- first_name: Fabian
  full_name: Portmann, Fabian
  last_name: Portmann
citation:
  ama: Lundholm D, Nam P, Portmann F. Fractional Hardy–Lieb–Thirring and related Inequalities
    for interacting systems. <i>Archive for Rational Mechanics and Analysis</i>. 2016;219(3):1343-1382.
    doi:<a href="https://doi.org/10.1007/s00205-015-0923-5">10.1007/s00205-015-0923-5</a>
  apa: Lundholm, D., Nam, P., &#38; Portmann, F. (2016). Fractional Hardy–Lieb–Thirring
    and related Inequalities for interacting systems. <i>Archive for Rational Mechanics
    and Analysis</i>. Springer. <a href="https://doi.org/10.1007/s00205-015-0923-5">https://doi.org/10.1007/s00205-015-0923-5</a>
  chicago: Lundholm, Douglas, Phan Nam, and Fabian Portmann. “Fractional Hardy–Lieb–Thirring
    and Related Inequalities for Interacting Systems.” <i>Archive for Rational Mechanics
    and Analysis</i>. Springer, 2016. <a href="https://doi.org/10.1007/s00205-015-0923-5">https://doi.org/10.1007/s00205-015-0923-5</a>.
  ieee: D. Lundholm, P. Nam, and F. Portmann, “Fractional Hardy–Lieb–Thirring and
    related Inequalities for interacting systems,” <i>Archive for Rational Mechanics
    and Analysis</i>, vol. 219, no. 3. Springer, pp. 1343–1382, 2016.
  ista: Lundholm D, Nam P, Portmann F. 2016. Fractional Hardy–Lieb–Thirring and related
    Inequalities for interacting systems. Archive for Rational Mechanics and Analysis.
    219(3), 1343–1382.
  mla: Lundholm, Douglas, et al. “Fractional Hardy–Lieb–Thirring and Related Inequalities
    for Interacting Systems.” <i>Archive for Rational Mechanics and Analysis</i>,
    vol. 219, no. 3, Springer, 2016, pp. 1343–82, doi:<a href="https://doi.org/10.1007/s00205-015-0923-5">10.1007/s00205-015-0923-5</a>.
  short: D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis
    219 (2016) 1343–1382.
corr_author: '1'
date_created: 2018-12-11T11:53:05Z
date_published: 2016-03-01T00:00:00Z
date_updated: 2025-09-18T10:52:35Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00205-015-0923-5
ec_funded: 1
external_id:
  arxiv:
  - '1501.04570'
  isi:
  - '000368535400010'
intvolume: '       219'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1501.04570
month: '03'
oa: 1
oa_version: Submitted Version
page: 1343 - 1382
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Archive for Rational Mechanics and Analysis
publication_status: published
publisher: Springer
publist_id: '5542'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 219
year: '2016'
...