Hardy type inequalities in weighted Herz-Morrey-Orlicz spaces

We prove Hardy-Sobolev inequalities in weighted Herz-Morrey-Orlicz spaces on Rⁿ R n . As an application, we discuss Hardy-Sobolev inequalities for generalized Riesz potentials aligned & Rα ,mf(x) = ∫ _ Rⁿ Rα ,m (x,y) f(y) dy, aligned R α , m f ( x ) = ∫ R n R α , m ( x , y ) f ( y ) d y , where Rα(x)=|x|α -n R α ( x ) = | x | α - n and Rα ,m(x,y) = Rα(x-y) - ∑ | | ≤ m-1 x !(DRα)(-y). R α , m ( x , y ) = R α ( x - y ) - ∑ | ℓ | ≤ m - 1 x ℓ ℓ ! ( D ℓ R α ) ( - y ) .