Best constant and value of extremizers for a k-plane transform inequality
arXiv:1111.5061 · doi:10.2140/apde.2014.7.1237
Abstract
The k-plane transform acting on test functions on R^d satisfies a dilation-invariant L^p to L^q inequality for some exponents p,q. We will explicit some extremizers and the value of the best constant for any value of k and d, solving the limit case of a 1997 conjecture from Baernstein and Loss. This extends their own result for k=2 and Christ's result for k=d-1.