The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (404 KB) | Metadata | Table of Contents | ZAA summary
Volume 40, Issue 3, 2021, pp. 313–347
DOI: 10.4171/ZAA/1687

Published online: 2021-06-24

Complex interpolation of Besov-type spaces on domains

Ciqiang Zhuo[1]

(1) Hunan Normal University, Changsha, China

Let $\Omega\subset\mathbb{R}^d$ ($d\geq 2$) be a bounded Lipschitz domain. In this article, the author mainly studies complex interpolation of Besov-type spaces on the domain $\Omega$, namely, we investigate the interpolation $$ [B_{p_0,q_0}^{s_0,\tau_0}(\Omega),B_{p_1,q_1}^{s_1,\tau_1}(\Omega)]_\Theta = B_{p,q}^{\diamond s,\tau}(\Omega) $$ under certain conditions on the parameters, where $B_{p,q}^{\diamond s,\tau}(\Omega)$ 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 $B_{p,q}^{\diamond s,\tau}(\mathbb{R}^d)$ 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 $\Omega=\mathbb{R}^d$.

Keywords: Besov-type space, diamond space, extension operator, Lipschitz domains, complex interpolation

Zhuo Ciqiang: Complex interpolation of Besov-type spaces on domains. Z. Anal. Anwend. 40 (2021), 313-347. doi: 10.4171/ZAA/1687