Suppose that is a linear or a sublinear operator which satisfies for any with compact support and
where is independent of and . For a function , suppose that is a commutator generated by and satisfies for any with compact support and
where is independent of and .
Let be a positive measurable function on and . We denote by the generalized Morrey space of all functions with finite quasinorm
Also, by we denote the weak generalized Morrey space of all functions for which
The authors prove the boundedness of the sublinear operator satisfying condition (1) generated by the Calderón-Zygmund operator from one generalized Morrey space to another space for and from to the weak space . When , they find a sufficient condition on the pair which ensures the boundedness of the commutator from to for . Finally, they apply their results to several particular operators such as pseudodifferential operators, the Littlewood-Paley operator, the Marcinkiewicz operator, and the Bochner-Riesz operator.