Weighted Boundedness Of Maximal Fractional Operator With Rough Kernal

The theory of A_p weight functions and the weighted spaces is an important branch of harmonic analysis. Lu Shanzhen and Yang Dachun firstly introduced the weighted Herz space and studied its theory and applications.In this dissertation, some boundedness of Calderón-Zygmund operator, fractional integral operator and fractional integral operator with rough kernal on weighted Herz-Morrey spaces and weighted Herz spaces are established.In the first chapter, we firstly introduce the properties of weighted Herz spaces, then we establish the boundedness of fractional integral operators and maximal fractional operator with rough kernal on the weighted Herz spaces.In the second chapter, the Weighted Herz-Morrey spaces are introduced and the estimates for Calderón-Zygmund operators on the weighted Herz-Morrey spaces are studied.In the third chapter, based on the second chapter, we will study the boundedness of fractional intergral operator and maximal fractional operator with rough kernal on the weighted Herz-Morrey space.