#### Vol. 7, No. 6, 2014

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Sharp constant for a $k$-plane transform inequality

### Alexis Drouot

Vol. 7 (2014), No. 6, 1237–1252
##### Abstract

The $k$-plane transform ${\mathsc{ℛ}}_{k}$ acting on test functions on ${ℝ}^{d}$ satisfies a dilation-invariant ${L}^{p}\to {L}^{q}$ inequality for some exponents $p,q$. We will make explicit some extremizers and the value of the best constant for any value of $k$ and $d$, solving the endpoint case of a conjecture of Baernstein and Loss. This extends their own result for $k=2$ and Christ’s result for $k=d-1$.

##### Keywords
k-plane transform, best constant, extremizers
Primary: 44A12