Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

Abstract

We consider the commutators [b, T] and $$[b,I_{\rho }]$$ on Orlicz-Morrey spaces, where T is a Calderón-Zygmund operator, $$I_{\rho }$$ is a generalized fractional integral operator and b is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness of the commutators on Orlicz-Morrey spaces. To do this we prove the boundedness of generalized fractional maximal operators on Orlicz-Morrey spaces. Moreover, we introduce Orlicz-Campanato spaces and establish their relations to Orlicz-Morrey spaces.