An Endpoint Estimate for Certain k-Plane Transforms
- 1 March 1986
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 29 (1) , 96-101
- https://doi.org/10.4153/cmb-1986-018-3
Abstract
In this paper we extend a result of Oberlin and Stein on Radon Transforms to /c-plane transforms for Specifically letwhere the supremum is taken over all affine k-planes ∏ parallel to the vector k-plane π. We show that F is in Ln of the Grassmann manifold Gn,k whenever f is in the Lorentz space L(n/k, 1) of ℝn. The proof relies very heavily on the ideas of M. Christ.Keywords
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