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2014 Sharp constant for a $k$-plane transform inequality
Alexis Drouot
Anal. PDE 7(6): 1237-1252 (2014). DOI: 10.2140/apde.2014.7.1237

Abstract

The k-plane transform k acting on test functions on d satisfies a dilation-invariant LpLq 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=d1.

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Alexis Drouot. "Sharp constant for a $k$-plane transform inequality." Anal. PDE 7 (6) 1237 - 1252, 2014. https://doi.org/10.2140/apde.2014.7.1237

Information

Received: 27 January 2012; Revised: 3 June 2014; Accepted: 27 August 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1310.44003
MathSciNet: MR3270163
Digital Object Identifier: 10.2140/apde.2014.7.1237

Subjects:
Primary: 44A12

Keywords: best constant , extremizers , k-plane transform

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 6 • 2014
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