On the Riesz Potential and Its Commutators on Generalized Orlicz-Morrey Spaces. (21st January 2014) - Guliyev, Vagif S.; Deringoz, Fatih
Abstract : We consider generalized Orlicz-Morrey spacesM Φ, φ ( ℝ n ) including their weak versionsW M Φ, φ ( ℝ n ) . In these spaces we prove the boundedness of the Riesz potential fromM Φ, φ 1 ( ℝ n ) toM Ψ, φ 2 ( ℝ n ) and fromM Φ, φ 1 ( ℝ n ) toW 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 ofφ 1 ( x, r ), φ 2 ( x, r ) inr .