Drouot, Alexis Sharp constant for a \(k\)-plane transform inequality. (English) Zbl 1310.44003 Anal. PDE 7, No. 6, 1237-1252 (2014). Summary: The \(k\)-plane transform \(\mathcal R_k\) acting on test functions on \(\mathbb R^d\) 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 A. Baernstein II and M. Loss [Rend. Semin. Mat. Fis. Milano 67, 9–26 (1997; Zbl 1016.44002)]. This extends their own result for \(k=2\) and M. Christ’s result [“Quasiextremals for a Radon-like transform”, Preprint, arXiv:1106.0722; “On extremals for a Radon-like transform”, Preprint, arXiv:1106.0728; “Extremizers of a Radon transform inequality”, Preprint, arXiv:1106.0719] for \(k=d-1\). Cited in 7 Documents MSC: 44A12 Radon transform Keywords:\(k\)-plane transform; best constant; extremizers Citations:Zbl 1016.44002 PDF BibTeX XML Cite \textit{A. Drouot}, Anal. PDE 7, No. 6, 1237--1252 (2014; Zbl 1310.44003) Full Text: DOI arXiv OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.