Fund Project:the North China Electric Power University Youth Foundation (No.200611004); the Renmin University of China Science Research Foundation (No.30206104).
The authors introduce the homogeneous Morrey-Herz spaces and the weak homogeneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in homogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators, Calder\'on-Zygmund operators and fractional integral operators. Furthermore, some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained. Moreover, the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calder\'on-Zygmund operators or fractional integral operators with RBMO$(\mu)$ functions.
