Characterizations for the Riesz potential and its commutators on generalized Orlicz-Morrey spaces

Abstract

Abstract In the present paper, we shall give a characterization for the Spanne and Adams type boundedness of the Riesz potential and its commutators on the generalized Orlicz-Morrey spaces, respectively. Also we give criteria for the weak versions of Spanne and Adams type boundedness of the Riesz potential on the generalized Orlicz-Morrey spaces. In all the cases the conditions for the boundedness are given in terms of Zygmund type integral inequalities involving the Young function Φ ( u ) $\Phi(u)$ and the function φ ( x , r ) $\varphi(x,r)$ defining the space.

Keywords

• generalized Orlicz-Morrey space
• Riesz potential
• commutator
• BMO