Reverse conformally invariant Sobolev inequalities on the sphere
- Resource Type
- Working Paper
- Authors
- Frank, Rupert L.; König, Tobias; Tang, Hanli
- Source
- J. Funct. Anal. 282 (2022), 109339
- Subject
- Mathematics - Analysis of PDEs
- Language
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 $n\geq 2$.