Multilinear fractional integral operators on non-homogeneous metric   measure spaces
  Let $(X,d,\mu)$ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions. In this paper, the boundedness of multilinear fractional integral operator in this setting is proved. Via a sharp maximal operator, the boundedness of commutators generated by multilinear fractional integral operator with $RBMO(\mu)$ function on non-homogeneous metric measure spaces in Lebesgue spaces is obtained. 
Huajun Gong, Rulong Xie, Chen Xu
math.CA