Strongly singular integrals along curves

Abstract

In this article we obtain $L^2$ bounds for strongly singular integrals along curves in ${\mathbb{R}}^d;$ our results both generalise and extend to higher dimensions those obtained by Chandarana in the plane. Moreover, we show that the operators in question are bounded from $L\log L$ to weak $L^1$ at the critical exponent $\alpha =0.$

10 pages