Boundedness Of Commutators Of Campanato Functions

Firstly, we stated the definitions of θ type Calderon-Zygmund operators and Campanato functions. Based on the atomic decomposition of Herz type Hardy spaces, by using the Jensen and Holder inequalities, the boundedness of commutators generated by θ type Calderon-Zygmund operators and Campanato functions from homogeneous Herz type Hardy spaces to homogeneous Herz spaces is obtained. Secondly, the concept and theory of homogeneous Morrey-Herz spaces are introduced. With the annular decomposition, the boundedness of commutators generated by θ type Calderon-Zygmund operators and Cam-panato functions on the homogeneous Morrey-Herz space is proved. In the last part, the fractional integral operators associated with differential operator are studied. Then, the boundedness of the commutators generated by frac-tional integral operators associated with operators and Campanato functions from homogeneous Herz spaces to homogeneous Herz spaces is showed. And we also proved that the commutators are bounded on homogeneous Morrey-Herz spaces.