Boundedness of commutators for multilinear Calder\'{o}n-Zygmund operators on Generalized Morrey Spaces

Abstract

Let $T$ be a $m$-linear Calder\'{o}n-Zygmund operator of type $\omega$ with $\omega$ being nondecreasing and $\omega \in$ Dini(1) and $[\vec{b},\,T]$ be the commutator generated by $T$ with symbols $\vec{b}=(b_1,\,\ldots,\,b_m)$ belonging to generalized Campanato spaces. We give necessary and sufficient conditions for the boundedness of $[\vec{b},\,T]$ on generalized Morrey spaces with variable growth condition.