Published February 15, 2022
| Submitted
Journal Article
Open
Reverse conformally invariant Sobolev inequalities on the sphere
- Creators
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Frank, Rupert L.
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König, Tobias
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Tang, Hanli
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.
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.Attached Files
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Additional details
- Eprint ID
- 111208
- Resolver ID
- CaltechAUTHORS:20211004-232831449
- DMS-1363432
- NSF
- DMS-1954995
- NSF
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft (DFG)
- Studienstiftung des deutschen Volkes
- ANR-18-CE40-002
- Agence Nationale pour la Recherche (ANR)
- 11701032
- National Natural Science Foundation of China
- 2020YFA0712900
- National Key Research and Development Program of China
- Created
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2021-10-07Created from EPrint's datestamp field
- Updated
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2021-12-14Created from EPrint's last_modified field