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Let k, N ∈ N with 1 ≤ k ≤ N and let Ω = Ω1 × Ω2 be an open set in Rk × RN−k. For p ∈ (1, ∞) and q ∈ (0, ∞), we consider the following weighted Sobolev type inequality: f Ω |g1(y)