Complex interpolation of function spaces with general weights

We present the complex interpolation of Besov and Triebel--Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel--Lizorkin spaces. As a corollary of our results, we obtain the complex interpolation between the weighted Triebel--Lizorkin spaces Ḟ_p₀,q₀^s₀ (ω ₀) and Ḟ_∞ ,q₁^s₁(ω ₁) with suitable assumptions on the parameters s₀,s₁,p₀, q₀ and q₁, and the pair of weights (ω ₀,ω ₁).