--- res: bibo_abstract: - We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Rupert foaf_name: Frank, Rupert L foaf_surname: Frank - foaf_Person: foaf_givenName: Robert foaf_name: Robert Seiringer foaf_surname: Seiringer foaf_workInfoHomepage: http://www.librecat.org/personId=4AFD0470-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-6781-0521 bibo_doi: 10.1016/j.jfa.2008.05.015 bibo_issue: '12' bibo_volume: 255 dct_date: 2008^xs_gYear dct_publisher: Academic Press@ dct_title: Non-linear ground state representations and sharp Hardy inequalities@ ...