  The classical criterion for compactness in Banach spaces of functions can be
reformulated into a simple tightness condition in the time-frequency domain.
This description preserves more explicitly the symmetry between time and
frequency than the classical conditions. The result is first stated and proved
for L^2(R^d), and then generalized to coorbit spaces. As special cases, we
obtain new characterizations of compactness in Besov-Triebel-Lizorkin spaces,
modulation spaces and Bargmann-Fock spaces.
