Mixed norm estimates for the k-plane transform
The Radon transform constitutes a fundamental concept for x-rays in medical imaging, and more generally, in image reconstruction problems from diverse fields. The Radon transform in Euclidean spaces assigns to functions their integrals over all affine hyperplanes. This transform can be generalized so that the integration is performed on affine k-dimensional subspaces; the corresponding transform is called k-plane transform. In this talk we will discuss sharp mixed norm inequalities for the k-plane transform when acting on radial functions and for potential-like operators supported in k-planes. This is joint work with Javier Duoandikoetxea and Osane Oruetxebarria.