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Reverse conformally invariant Sobolev inequalities on the sphere

Frank, Rupert L. and König, Tobias and Tang, Hanli (2021) Reverse conformally invariant Sobolev inequalities on the sphere. Journal of Functional Analysis . ISSN 0022-1236. doi:10.1016/j.jfa.2021.109339. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20211004-232831449

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Abstract

We consider the optimization problem corresponding to the sharp constant in a conformally invariant Sobolev inequality on the n-sphere involving an operator of order 2s > n. In this case the Sobolev exponent is negative. Our results extend existing ones to noninteger values of s and settle the question of validity of a corresponding inequality in all dimensions n ≥ 2.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jfa.2021.109339DOIArticle
https://arxiv.org/abs/2105.05141arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
König, Tobias0000-0002-8808-897X
Tang, Hanli0000-0001-8060-9884
Additional Information:© 2021 Elsevier Inc. Received 11 May 2021, Accepted 11 November 2021, Available online 30 November 2021. Partial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 and Deutsche Forschungsgemeinschaft grant EXC-2111-390814868 (R.L.F.), Studienstiftung des deutschen Volkes and ANR BLADE-JC ANR-18-CE40-002 (T.K.) and National Natural Science Foundation of China (Grant No. 11701032) and National Key Research and Development Program of China (Grant No. 2020YFA0712900) (H.T.) is acknowledged.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
NSFDMS-1954995
Deutsche Forschungsgemeinschaft (DFG)EXC-2111-390814868
Studienstiftung des deutschen VolkesUNSPECIFIED
Agence Nationale pour la Recherche (ANR)ANR-18-CE40-002
National Natural Science Foundation of China11701032
National Key Research and Development Program of China2020YFA0712900
DOI:10.1016/j.jfa.2021.109339
Record Number:CaltechAUTHORS:20211004-232831449
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20211004-232831449
Official Citation:Rupert L. Frank, Tobias König, Hanli Tang, Reverse conformally invariant Sobolev inequalities on the sphere, Journal of Functional Analysis, 2021, 109339, ISSN 0022-1236, https://doi.org/10.1016/j.jfa.2021.109339.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111208
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:07 Oct 2021 19:21
Last Modified:30 Nov 2021 21:32

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