  For any bounded convex domain $\Omega$ with $C^{2}$ boundary in
$\mathbb{C}^{n}$, we show that there exist positive constants $C_{1}$ and
$C_{2}$ such that \[
C_{1}\sqrt{\dfrac{K\left(w,w\right)}{\delta\left(w\right)}}\leq\left\Vert
K\left(\cdot,w\right)\right\Vert _{L^{2}\left(\partial\Omega\right)}\leq
C_{2}\sqrt{\dfrac{K\left(w,w\right)}{\delta\left(w\right)}}, \] for any
$w\in\Omega$. Here $K$ is the Bergman kernel of $\Omega$, and $\delta$ is the
distance-to-boundary function.
