  In this paper, the author introduces parabolic generalized local Morrey
spaces and gets the boundedness of a large class of parabolic rough operators
on them. The author also establihes the parabolic local Campanato space
estimates for their commutators on parabolic generalized local Morrey spaces.
As its special cases, the corresponding results of parabolic sublinear
operators with rough kernel and their commutators can be deduced, respec-
tively. At last, parabolic Marcinkiewicz operator which satisfies the
conditions of these theorems can be considered as an example.
