Parameterized Littlewood-Paley Operators On Herz-Morrey Spaces With Variable Exponents

In this dissertation,we mainly investigate the boundedness of parameterized Littlewood-Paley operators with rough kernel and their commutators on some HerzMorrey type spaces with variable exponents.The main results are stated as follows.In the chapter 1,with the help of the boundedness of Lebesgue space with variable exponent,by applying hierarchical decomposition of function and real-variable techniques,the boundedness of parameterized Marcinkiewicz integral,area integral and Littlewood-Paley g_λ~*function with rough kernel is obtained on grand variable Herz spaces.Meanwhile,the boundedness of higher order commutators generated by the area integral and Littlewood-Paley g_λ~*function is also proved.In the chapter 2,by means of the properties of variable exponent Ap(·)weight,combined with the method of function decomposition and the generalized Holder inequality,the weighted boundedness of parameterized area integral,LittlewoodPaley g_λ~*function with rough kernel and their higher order commutators generated by BMO functions and Lipschitz functions on Herz-Morrey spaces with variable exponents is given.In the chapter 3,through the definition of generalized variable exponent Morrey space,by using the real method of harmonic analysis,the boundedness of Marcinkiewicz integral with rough kernel and a kind of multilinear commutator generated by BMO functions is obtained on generalized variable exponent Morrey spaces.At the same time,we also consider the boundedness of parameterized Marcinkiewicz integral with rough kernel and its higher order commutator.