A note on the boundedness of discrete commutators on Morrey spaces and   their preduals
  Dyadic fractional integral operators are shown to be bounded on Morrey spaces and their preduals. It seems that the proof of the boundedness by means of dyadic fractional integral operators is effective particularly on the preduals. In the present paper the commutators are proved to be bounded as well. 
Yoshihiro Sawano
math.FA