Let () be a bounded Lipschitz domain. In this article, the author mainly studies complex interpolation of Besov-type spaces on the domain , namely, we investigate the interpolation
under certain conditions on the parameters, where denotes the so-called diamond space associated with the Besov-type space. To this end, we first establish the equivalent characterization of the diamond space in terms of Littlewood–Paley decomposition and differences. Via some examples, we also show that this interpolation result does not hold under some other assumptions on the parameters or when .
Cite this article
Ciqiang Zhuo, Complex interpolation of Besov-type spaces on domains. Z. Anal. Anwend. 40 (2021), no. 3, pp. 313–347DOI 10.4171/ZAA/1687