Abstract: By using  the weight estimation of A_p and the function decompositions method, and by means of the weighted estimation on the  L^p spaces, we proved the weighted boundedness of the intrinsic square functions, intrinsic Littlewood-Paley  g and g^*_λfunctions on the generalized fractional  Morrey spaces, and gave the weighted boundedness of the corresponding BMO commutators.

Key words:  , intrinsic square function, commutator, generalized fractional , Morrey space, weighted boundedness