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

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

2011-11-21

arxiv.org/abs/1111.5061v5

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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