Reverse conformally invariant Sobolev inequalities on the sphere

Frank, Rupert L. ; Konig, Tobias and Tang, Hanli (2022): Reverse conformally invariant Sobolev inequalities on the sphere. In: Journal of Functional Analysis, Vol. 282, No. 4, 109339

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 sand settle the question of validity of a corresponding inequality in all dimensions n >= 2. (c) 2021 Elsevier Inc. All rights reserved.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-1236
• Language: English