  In this paper, we give necessary conditions and sufficient conditions
respectively for the boundedness of the singular integral operator on the
weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey
spaces; the $A_q$-theory by Muckenhoupt and Wheeden does not suffice. We also
discuss the boundedness of the commutators. The difference between the maximal
operator and the singular integral operators will be clarified. Further, the
property of the sharp maximal operator is investigated.
