Weak-type Fefferman-Stein inequality and commutators on weak Orlicz-Morrey spaces

We consider the Fefferman-Stein inequality for weak Orlicz-Morrey spaces and the commutators [b,T]$[b,T]$ and [b,I rho]$[b,I_{\rho }]$ on weak Orlicz-Morrey spaces, where T is a Calderon-Zygmund operator, I rho$I_{\rho }$ 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 from of [b,T]$[b,T]$ and [b,I rho]$[b,I_{\rho }]$ from a weak Orlicz Morrey space to another weak Orlicz-Morrey space. We use the Fefferman-Stein inequality to prove the boundedness of the commutators. Since weak Orlicz-Morrey spaces contain the weak Lebesgue, weak Orlicz and weak Morrey spaces as special cases, our results contain the bounedness on these function spaces which are also new results.