Commutators of Calderón–Zygmund and generalized fractional integral operators on generalized Morrey spaces

Abstract

We consider the commutators [b, T] and $$[b,I_{\rho }]$$ , where T is a Calderon–Zygmund operator, $$I_{\rho }$$ is a generalized fractional integral operator and b is a function in generalized Campanato spaces with variable growth condition. We give necessary and sufficient conditions for the boundedness of the commutator on generalized Morrey spaces with variable growth condition.