Parabolic sublinear operators with rough kernel generated by parabolic   Calder\'on-Zygmund operators and parabolic local Campanato space estimates   for their commutators on the parabolic generalized local Morrey spaces
  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. 
Ferit Gurbuz
math.AP