A note on restricted X-ray transforms

Abstract

We show how the techniques introduces by Christ can be employed to derive endpoint $L^p-L^q$ bounds for the X-ray transform associated to the line complex generated by the curve $t\to (t,t^2,...,t^{d-1}).$ Almost-sharp Lorentz space estimates are produced as well.

11 pages

Cited by in corpus (1)

• Sharp Sobolev regularity of restricted X-ray transforms