  In this paper, we obtain two interpolation theorems on convex-set valued
Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and
Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively.
As applications, we obtain the boundedness of convex-set valued fractional
averaging operators and fractional maximal operators, and prove the reverse
factorization property of matrix weights.
