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