Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

https://doi.org/10.1016/j.jfa.2014.10.012Get rights and content
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Abstract

We establish endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euclidean arclengths. We also explore the behavior of certain natural interpolants and extrapolants of the affine and Euclidean versions of these operators.

Keywords

Generalized Radon transforms
Affine arclength
Geometric inequalities

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