On the Riesz Potential and Its Commutators on Generalized Orlicz-Morrey Spaces

Abstract EN

We consider generalized Orlicz-Morrey spaces M Φ , φ ( ℝ n ) including their weak versions W M Φ , φ ( ℝ n ) .

In these spaces we prove the boundedness of the Riesz potential from M Φ , φ 1 ( ℝ n ) to M Ψ , φ 2 ( ℝ n ) and from M Φ , φ 1 ( ℝ n ) to W M Ψ , φ 2 ( ℝ n ) .

As applications of those results, the boundedness of the commutators of the Riesz potential on generalized Orlicz-Morrey space is also obtained.

In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on ( φ 1 , φ 2 ) , which do not assume any assumption on monotonicity of φ 1 ( x , r ) , φ 2 ( x , r ) in r .