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An Endpoint Estimate for Certain k-Plane Transforms

Published online by Cambridge University Press:  20 November 2018

S. W. Drury
S. W. Drury*
Affiliation:
McGill University, Montreal, Quebec
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Abstract

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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.

Keywords

44A15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 96 - 101
Copyright
Copyright © Canadian Mathematical Society 1986

References

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