Geodesic
Complex interpolation of function spaces with general weights
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 289-320.

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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 $(\omega _{0},\omega _{1})$.
DOI : 10.14712/1213-7243.2024.003
Classification : 26B35, 42B25, 42B35, 46E35
Keywords: Besov space; Triebel--Lizorkin space; complex interpolation; Muckenhoupt class 
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Drihem, Douadi. Complex interpolation of function spaces with general weights. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 289-320. doi : 10.14712/1213-7243.2024.003. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.003/

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