  The aim of this paper is to get the boundedness of certain multi-sublinear
operators generated by multilinear fractional integral operators on the product
generalized local Morrey spaces under generic size conditions which are
satisfied by most of the operators in harmonic analysis. We also prove that the
commutators of multilinear operators generated by local campanato functions and
multilinear fractional integral operators are also bounded on the product
generalized local Morrey spaces.
