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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)

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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 Paper
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.
Funding AgencyGrant Number
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
Record Number:CaltechAUTHORS:20211004-232831449
Persistent URL:
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,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111208
Deposited By: George Porter
Deposited On:07 Oct 2021 19:21
Last Modified:30 Nov 2021 21:32

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