Abstract 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 & R, ₌f (x) = ₑⁿ R, ₌ (x, y) f (y) dy, aligned R α, m f (x) = ∫ R n R α, m (x, y) f (y) d y, where R (x) =|x|^ -n R α (x) = | x | α - n and R, ₌ (x, y) = R (x-y) - | | ₌-₁ x^{ ! (D^ R) (-y) }. R α, m (x, y) = R α (x - y) - ∑ | ℓ | ≤ m - 1 x ℓ ℓ ! (D ℓ R α) (- y).
Mizuta et al. (Sat,) studied this question.