JournalszaaVol. 40, No. 3pp. 313–347

Complex interpolation of Besov-type spaces on domains

  • Ciqiang Zhuo

    Hunan Normal University, Changsha, China
Complex interpolation of Besov-type spaces on domains cover
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Abstract

Let ΩRd\Omega\subset\mathbb{R}^d (d2d\geq 2) be a bounded Lipschitz domain. In this article, the author mainly studies complex interpolation of Besov-type spaces on the domain Ω\Omega, namely, we investigate the interpolation

[Bp0,q0s0,τ0(Ω),Bp1,q1s1,τ1(Ω)]Θ=Bp,qs,τ(Ω)[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 Bp,qs,τ(Ω)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 Bp,qs,τ(Rd)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 Ω=Rd\Omega=\mathbb{R}^d.

Cite this article

Ciqiang Zhuo, Complex interpolation of Besov-type spaces on domains. Z. Anal. Anwend. 40 (2021), no. 3, pp. 313–347

DOI 10.4171/ZAA/1687