Mixed-norm estimates for the k-plane transform
نویسنده
چکیده
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 affine hyperplanes. This can be extended so that the integration is performed on affine k-dimensional subspaces, the corresponding transform is called k-plane transform. An overview of mixed-norm inequalities for the k-plane transform and related potential-type operators supported on k-planes is presented. Particular attention is given to the action of these operators on classes of radial functions and applications to bounds for the Kakeya maximal operator are discussed.
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