--- _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”." 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. Archive for Rational Mechanics and Analysis. 2016;219(3):1343-1382. doi:10.1007/s00205-015-0923-5 apa: Lundholm, D., Nam, P., & Portmann, F. (2016). Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. Springer. https://doi.org/10.1007/s00205-015-0923-5 chicago: Lundholm, Douglas, Phan Nam, and Fabian Portmann. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics and Analysis. Springer, 2016. https://doi.org/10.1007/s00205-015-0923-5. ieee: D. Lundholm, P. Nam, and F. Portmann, “Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems,” Archive for Rational Mechanics and Analysis, 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.” Archive for Rational Mechanics and Analysis, vol. 219, no. 3, Springer, 2016, pp. 1343–82, doi:10.1007/s00205-015-0923-5. short: D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis 219 (2016) 1343–1382. date_created: 2018-12-11T11:53:05Z date_published: 2016-03-01T00:00:00Z date_updated: 2021-01-12T06:52:04Z day: '01' department: - _id: RoSe doi: 10.1007/s00205-015-0923-5 ec_funded: 1 intvolume: ' 219' 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 219 year: '2016' ...