Endpoint bounds for a generalized {R}adon transform

Details Endpoint bounds for a generalized {R}adon transform Endpoint bounds for a generalized {R}adon transform

2009-05-24

arxiv.org/abs/0905.3926v1

Mathematics

Classical Analysis and ODEs

24 pages, The final version of this article will appear in the Journal of the London Math. Soc

Scientific paper

We prove that convolution with affine arclength measure on the curve
parametrized by $h(t) := (t,t^2,...,t^n)$ is a bounded operator from
$L^p(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$ for the full conjectured range of
exponents, improving on a result due to M. Christ. We also obtain nearly sharp
Lorentz space bounds.

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