{"date_published":"2016-03-01T00:00:00Z","publication_status":"published","month":"03","oa_version":"Submitted Version","publisher":"Springer","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"}],"language":[{"iso":"eng"}],"page":"1343 - 1382","date_created":"2018-12-11T11:53:05Z","scopus_import":1,"publication":"Archive for Rational Mechanics and Analysis","_id":"1622","status":"public","day":"01","oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","volume":219,"year":"2016","department":[{"_id":"RoSe"}],"quality_controlled":"1","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."}],"issue":"3","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"type":"journal_article","title":"Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems","intvolume":"       219","doi":"10.1007/s00205-015-0923-5","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>","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.","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>.","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.","short":"D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis 219 (2016) 1343–1382.","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>."},"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”.","publist_id":"5542","main_file_link":[{"url":"http://arxiv.org/abs/1501.04570","open_access":"1"}],"ec_funded":1,"date_updated":"2021-01-12T06:52:04Z"}