Sharp Sobolev regularity of restricted X-ray transforms

Abstract

We study $L^p$-Sobolev regularity estimate for the restricted X-ray transforms generated by nondegenerate curves. Making use of the inductive strategy in the recent work by the authors, we establish the sharp $L^p$-regularity estimates for the restricted X-ray transforms in ${\mathbb{R}}^{d+1}$, $d\ge 3$. This extends the result due to Pramanik and Seeger in ${\mathbb{R}}^3$ to every dimension.

18 pages

References in corpus (3)

• Compactness Properties of Weighted Summation Operators on Trees
• Sharp $L^p$ bounds for the helical maximal function
• $L^p$ Regularity Estimates for a Class of Integral Operators with Fold Blowdown Singularities