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

We consider generalized orlicz-morrey spaces mφ,∝ (ℝn) including their weak versions wmφ,∝ (ℝn). in these spaces we prove the boundedness of the riesz potential from mφ,∝1(ℝn) to mψ,∝2(ℝn) and from mφ,∝1(ℝn) to wmψ,∝2(ℝn). 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 (∝1,∝2),which do not assume any assumption on monotonicity of ∝1(x,r),∝2(x,r) in r. © 2014 v. s. guliyev and f. deringoz.