--- _id: '2381' abstract: - lang: eng text: 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. author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Frank R, Seiringer R. Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. 2008;255(12):3407-3430. doi:10.1016/j.jfa.2008.05.015 apa: Frank, R., & Seiringer, R. (2008). Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2008.05.015 chicago: Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” Journal of Functional Analysis. Academic Press, 2008. https://doi.org/10.1016/j.jfa.2008.05.015. ieee: R. Frank and R. Seiringer, “Non-linear ground state representations and sharp Hardy inequalities,” Journal of Functional Analysis, vol. 255, no. 12. Academic Press, pp. 3407–3430, 2008. ista: Frank R, Seiringer R. 2008. Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis. 255(12), 3407–3430. mla: Frank, Rupert, and Robert Seiringer. “Non-Linear Ground State Representations and Sharp Hardy Inequalities.” Journal of Functional Analysis, vol. 255, no. 12, Academic Press, 2008, pp. 3407–30, doi:10.1016/j.jfa.2008.05.015. short: R. Frank, R. Seiringer, Journal of Functional Analysis 255 (2008) 3407–3430. date_created: 2018-12-11T11:57:20Z date_published: 2008-12-15T00:00:00Z date_updated: 2021-01-12T06:57:08Z day: '15' doi: 10.1016/j.jfa.2008.05.015 extern: 1 intvolume: ' 255' issue: '12' main_file_link: - open_access: '1' url: http://arxiv.org/abs/0803.0503 month: '12' oa: 1 page: 3407 - 3430 publication: Journal of Functional Analysis publication_status: published publisher: Academic Press publist_id: '4543' quality_controlled: 0 status: public title: Non-linear ground state representations and sharp Hardy inequalities type: journal_article volume: 255 year: '2008' ...