Let α > 0. We consider the linear span X_α(ℝ ⁿ) of scalar Riesz's kernels {1/|x-a|^α} aεℝⁿ and the linear span η_α(ℝ ⁿ of vector Riesz's kernels {1/|x-a|^α+1(x-a)} aεℝⁿ. We study the following problems. (1) When is the intersection X_α(ℝⁿ) ∩ L^p(ℝ ⁿ) dense in L^p(ℝⁿ)? (2) When is the intersection η_α(ℝⁿ) ∩ L ^p(ℝⁿ, ℝⁿ) dense in L ^p(ℝⁿ, ℝⁿ)?