LAUSR

In the present paper, we will characterize the boundedness of the generalized fractional integral operators $$I_{\rho }$$Iρ and the generalized fractional maximal operators $$M_{\rho }$$Mρ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators $$M_{\rho }$$Mρ and $$I_{\rho }$$Iρ on generalized Orlicz–Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators $$M_{\rho }$$Mρ and $$I_{\rho }$$Iρ on generalized Orlicz–Morrey spaces.