---
_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'
...