Boundedness of \(\theta\)-type Calderón-Zygmund operators and commutators in the generalized weighted Morrey spaces (Q340955)

Summary: 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 \(T_\theta\) 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.