Rough singular integrals associated to surfaces of revolution

Let $1<p<\infty$ and $n\ge 2$. The authors establish the $L^p(\mathbb{R}^{n+1})$-boundedness for a class of singular integral operators associated to surfaces of revolution, $\{(t,\phi(\vert t\vert)): t\in\mathbb{R}^n\}$, with rough kernels, provided that the corresponding maximal function along the plane curve $\{(t, \phi(\vert t\vert)): t\in\mathbb{R}\}$ is bounded on $L^p(\mathbb{R}^2)$.