Best constant and value of extremizers for a k-plane transform inequality

الأصل · EN

The k-plane transform acting on test functions on Rᵈ satisfies a dilation-invariant Lᵖ to Lq 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.