We study double Hilbert transforms and maximal functions along
surfaces of the form $(t_1,t_2,\gamma_1(t_1)\gamma_2(t_2))$. The
$L^p(\mathbb{R}^3)$ boundedness of the maximal operator is obtained
if each $\gamma_i$ is a convex increasing and $\gamma_i(0)=0$. The
double Hilbert transform is bounded in $L^p(\mathbb{R}^3)$ if both
$\gamma_i$'s above are extended as even functions. If $\gamma_1$ is
odd, then we need an additional comparability condition on
$\gamma_2$. This result is extended to higher dimensions and the
general hyper-surfaces of the form
$(t_1,\dots,t_{n},\Gamma(t_1,\dots,t_{n}))$ on $\mathbb{R}^{n+1}$.