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

Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind