  In this paper we prove mean curvature comparisons and volume comparisons on a
smooth metric measure space when the integral radial Bakry-\'Emery Ricci tensor
and the potential function or its gradient are bounded. As applications, we
prove diameter estimates and eigenvalue estimates on smooth metric measure
spaces. These results not only give a supplement of the author's previous
results under integral Bakry-\'Emery Ricci tensor bounds, but also are
generalizations of the Wei-Wylie's pointwise results.
