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

Abstract

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.