On the Riesz Potential and Its Commutators on Generalized Orlicz-Morrey Spaces. (21st January 2014) - Guliyev, Vagif S.
Abstract : 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 .