The -plane transform acting on test functions on satisfies a dilation-invariant inequality for some exponents . We will make explicit some extremizers and the value of the best constant for any value of and , solving the endpoint case of a conjecture of Baernstein and Loss. This extends their own result for and Christ’s result for .
"Sharp constant for a $k$-plane transform inequality." Anal. PDE 7 (6) 1237 - 1252, 2014. https://doi.org/10.2140/apde.2014.7.1237