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.