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We give characterizations of Besov and Triebel-Lizorkin spaces $B_{pq}^s\left(\Omega \right)$ and $F_{pq}^s\left(\Omega \right)$ in smooth domains $\Omega \subset {ℝ}^n$ via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.