  The Rogers-Shephard and Zhang's projection inequalities are two reverse,
affine isoperimetric inequalities relating the volumes of a convex body and its
difference body and polar projection body, respectively. Following a classical
work by Schneider, both inequalities have been extended to the so-called
higher-order setting. In this work, we establish the higher-order analogues for
these inequalities in the setting of log-concave functions.
