  This paper uses frame techniques to characterize the Schatten class
properties of integral operators. The main result shows that if the
coefficients of certain frame expansions of the kernel of an integral operator
are in (\ell^{2,p}), then the operator is Schatten p-class. As a corollary, we
conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential
operator lies in a particular mixed modulation space, then the operator is
Schatten p-class. Our corollary improves existing Schatten class results for
pseudodifferential operators and the corollary is sharp in the sense that
larger mixed modulation spaces yield operators that are not Schatten class.
