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An Endpoint Estimate for Certain k-Plane Transforms
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper we extend a result of Oberlin and Stein on Radon Transforms to /c-plane transforms for Specifically let
where 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.
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- Copyright © Canadian Mathematical Society 1986
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