  In this paper, we introduce a type of weighted multilinear Hardy operators
and obtain their sharp bounds on the product of Lebesgue spaces and central
Morrey spaces. In addition, we obtain sufficient and necessary conditions of
the weight functions so that the commutators of the weighted multilinear Hardy
operators (with symbols in central BMO space) are bounded on the product of
central Morrey spaces. These results are further used to prove sharp estimates
of some inequalities due to Riemann-Liouville and Weyl.
