University of Birmingham > Talks@bham > Analysis Seminar > On extremizers of certain inequalities for the k-plane transform

On extremizers of certain inequalities for the k-plane transform

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If you have a question about this talk, please contact José Cañizo.

The Radon transform is an integral transform with applications in mathematics, tomography, and medicine. The k-plane transform is an integral transform that maps a function to its integrals over all k-dimensional planes. When k=n-1, the k-plane transform and the Radon transform coincide.

The k-plane transform is a bounded operator from Lp of Euclidean space to Lq of the Grassman manifold of all affine k-planes for certain values of q and p. Extremizers have been determined in a few cases, but most remain open. In this talk, we will focus on showing that, in the endpoint case q=n+1, extremizers are unique. Rearrangement inequalities will be a key tool.

This talk is part of the Analysis Seminar series.

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