  We completely characterize the boundedness of the area operators from the
Bergman spaces $A^p_\alpha(\mathbb{B}_ n)$ to the Lebesgue spaces
$L^q(\mathbb{S}_ n)$ for all $0<p,q<\infty$. For the case $n=1$, some partial
results were previously obtained by Wu. Especially, in the case $q<p$ and
$q<s$, we obtain the new characterizations for the area operators to be
bounded. We solve the cases left open there and extend the results to
$n$-complex dimension.
