  We establish bounds on the decay of time-dependent multipoint correlation
functionals of one-dimensional quasi-free fermions in terms of the decay
properties of their two-point function. At a technical level, this is done with
the help of bounds on certain bordered determinants and pfaffians. These
bounds, which we prove, go beyond the well-known Hadamard estimates. Our main
application of these results is a proof of strong (exponential) dynamical
localization of spin-correlation functions in disordered $XY$-spin chains.
