The essential norm estimates of Hankel and the $\overline\partial$-Neumann operators

Compactness of the $\overline\partial$-Neumann operator is
closely connected to the compactness of Hankel operators on the Bergman
space. At first, for convex domains in $\mathbb{C}^n$, we use the
$\overline\partial$ methods to relate the compactness of a Hankel
operator to the boundary behavior of its symbol. In the absence of
compactness, we give the essential norm estimates of Hankel operators.
This in turn, led us to obtain the essential norm estimates for the
$\overline\partial$-Neumann operator on convex domains. (This is joint
work with Sonmez Sahutoglu)