Abstract: 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 \dot{F}_{p_{0},q_{0}}^{s_{0}} (\omega _{0}) and \dot{F}_{\infty ,q_{1}}^{s_{1}}(\omega _{1}) with suitable assumptions on the parameters s_{0},s_{1},p_{0}, q_{0} and q_{1}, and the pair of weights (\omega _{0},\omega _{1}).
Keywords: Besov space; Triebel-Lizorkin space; complex interpolation; Muckenhoupt class
DOI: DOI 10.14712/1213-7243.2024.003
AMS Subject Classification: 42B25 42B35 26B35 46E35