  We establish the $L^1$ weighted propagation properties for solutions of the
Boltzmann equation with hard potentials and non-integrable angular components
in the collision kernel. Our method identifies null forms by angular averaging
and deploys moment estimates of solutions to the Boltzmann equation whose
summability is achieved by introducing the new concept of Mittag-Leffler
moments - extensions of $L^1$ exponentially weighted norms. Such $L^1$ weighted
norms of solutions to the Boltzmann equation are, both, generated and
propagated in time and the characterization of their corresponding
Mittag-Leffler weights depends on the angular singularity and potential rates
in the collision kernel. These estimates are a fundamental step in order to
obtain $L^\infty$ exponentially weighted estimates for solutions of the
Boltzmann equation being developed in a follow up work.
