Littlewood-Paley Type Operators On Generalized Fractional Morrey Spaces

In this dissertation,we mainly research the weighted boundedness of the in-trinsic square functions and their commutators,the Littlewood-Paley operators with rough kernel and their commutators and the parameterized Littlewood-Paley oper-ators with rough kernel and their commutators on the generalized fractional Morrey spaces.The main works are stated as follows.First,by using the properties of weight function,the method of function hierar-chical decomposition and the tools of Minkowski's inequality,applying the weighted estimations of intrinsic square functions and their commutators on the Lebesgue s-paces,the weighted boundedness of intrinsic square functions and their commutators on the generalized fractional Morrey spaces are obtained.Second,as the kernel ? ? Lq(Sn-1)(1<q??)is homogeneous of degree zero and has a mean value zero on we prove that the boundedness of the Littlewood-Paley operators with rough kernel and their commutators on the gener-alized fractional weighted Morrey spaces.Third,we obtain that the weighted estimations of three classes of the param-eterized Littlewood-Paley operators with rough kernel(??,??? and ??*,?)and their commutators on the generalized fractional Morrey spaces as ? satisfies a class of the logarithmic type Lipschitz condition,respectively.