Boundedness Of The Littlewood-paley, Function In The Weak Herz-type Space

In this thesis, motivated by the results of Littlewood-Paley operators and Herz type spaces, we first introduce weighted weak Herz spaces and the de-composition theorem of the spaces. Then, according to the methods of real harmonic analysis, also by using the decompositons of function spaces and the properties of A1 weighted functions, the boundedness of the Littlewood-Paley operators and the commutators generated by Littlewood-Paley operators and BMO function on weighted weak Herz spaces are obtained. And basing on the studies of Lusin area function Sψ, on Herz type spaces, the boundedness of gλfunctions on weak Herz spaces is discussed. Similar to the results of Herz type spaces, at last, we prove that Littlewood-Paley g functions is bounded on weak Herz-Morrey spaces.