Research On Boundedness Of Intrinsic Littlewood-Paley Operators On Campanato Spaces And Weighted Morrey Spaces

The intrinsic Littlewood-Paley operators were first introducted by Wilson, which pointwise dominated all the classical square operators and are independent of any particular kernel. Wilson used these operators to solve a conjecture which proposed by R. Fefferman and E. M. Stein. Moreover, Wilson proved that these intrinsic square functions are bounded on the weighted Lebesgue spaces Lwp(Rn) when p ? (1, ?) and w?Ap(Rn). In this thesis, we mainly study the boundedness of intrinsic Littlewood-Paley operators on Campanato spaces and weighted Morrey spaces, including the in-trinsic square function, intrinsic Littlewood-Paley g-function and intrinsic Littlewood-Paley g?*-function. In the first chapter, we introduce some background of the relevant operators and spaces. In the second chapter and the third chapter, we study that if in-trinsic square function, intrinsic Littlewood-Paley g-function and intrinsic Littlewood-Paley g?*-function are finite for one point, then they are finite almost everywhere in Rn, and furthermore, the above operators are bounded on Campanato spaces, where the kernel function is generated by a class of functions which satisfy the Lipschitz condition. In the last chapter, when the Lipschitz condition is reduced to the Dini condition, we obtain the weak type estimates and boundedness of intrinsic square functions and their commutators on weighted Morrey spaces.