Boundedness of θ-Type Calderon-Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces

We first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space as special cases. Then, we discuss the strong-type and weak-type estimates for a class of Calderon-Zygmund type operators T-theta in these new Morrey type spaces. Furthermore, the strong-type estimate and endpoint estimate of commutators [b,T-theta] formed by b and T-theta are established. Also, we study related problems about two-weight, weak-type inequalities for T-theta and [b,T-theta] in the Morrey type spaces and give partial results.