  In this article, we introduce a class of multilinear fractional integral
operators with generalized kernels that are weaker than the Dini kernel
condition. We establish the boundedness of multilinear fractional integral
operators with generalized kernels on weighted Lebesgue spaces and variable
exponent Lebesgue spaces, as well as the boundedness of multilinear commutators
generated by multilinear fractional integral operators with generalized kernels
and $BMO$ functions. Even when the generalized kernels condition goes back to
the Dini kernel condition, the conclusions on the commutators remain new.
