Fractional Integral Operators Commutators Weighted Boundedness

Under the inspiration of the definitions of Morrey space and Herz spaces, we have the Morrey-Herz spaces. Basing on the Morrey space and Morrey-Herz spaces, we do further researches for the weighted Morrey-Herz space (?), and introduce the weightedλ－central Morrey space (?). Then by the properties of A_p weight function and the functional analysis and the harmonic analysis methods, we discuss and obtain the boundedness of the fractional integral operator commutators with rough kernel on weighted spaces (?) when these commutators satisfy some conditions. At the last, we introduce weighted CBMO functions, then the weighted boundedness of the classification commutators, which is formed by the fractional integral operators and CBMO function, is obtained on theλ－central Morrey space (?). These results have supplemented the certain theory of operators and its commutators.