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Journal of the London Mathematical Society Advance Access originally published online on July 17, 2009
Journal of the London Mathematical Society 2009 80(2):357-374; doi:10.1112/jlms/jdp033
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© 2009 London Mathematical Society

Endpoint bounds for a generalized Radon transform

Betsy Stovall

Department of Mathematics
University of California
Berkeley, CA 94720
USA

We prove that convolution with affine arclength measure on the curve parametrized by h(t) := (t, t2, ..., tn) is a bounded operator from Lp(Rn) to Lq(Rn) for the full conjectured range of exponents, improving on a result due to M. Christ. We also obtain nearly sharp Lorentz space bounds.

2000 Mathematics Subject Classification 42B10 (primary), 44A35, 44A12 (secondary).

The author was supported in part by NSF grant DMS-040126.

Received September 4, 2008; revised March 3, 2009; published online July 17, 2009.


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