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

Abstract

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 Calderón–Zygmund type operators Tθ in these new Morrey type spaces. Furthermore, the strong-type estimate and endpoint estimate of commutators [b,Tθ] formed by b and Tθ are established. Also, we study related problems about two-weight, weak-type inequalities for Tθ and [b,Tθ] in the Morrey type spaces and give partial results.