Abstract
In this paper, the authors first establish the boundedness of sublinear operators on the weighted Herz space with general weights. At the extreme case, the authors show these operators are bounded from the weighted Herz space to the weighted weak Herz space. Moreover, the authors also discuss the boundedness of the local Calderón-Zygmund operator of the non-convolution type on the weighted Herz-type Hardy spaces and show that these operators map the weighted Herz-type Hardy space into the weighted weak Herz-type Hardy space at the extreme case.
