In this paper we are concerned with Triebel-Lizorkin-Morrey spaces $\mathcal{E}^{s}_{u,p,q}(\Omega)$ of positive smoothness $s$ defined on (special or bounded) Lipschitz domains $\Omega\subset\mathbb{R}^d$ as well as on $\mathbb{R}^d$. For those spaces we prove new equivalent characterizations in terms of local oscillations which hold as long as some standard conditions on the parameters are fulfilled. As a byproduct, we also obtain novel characterizations of $\mathcal{E}^{s}_{u,p,q}(\Omega)$ using differences of higher order. Special cases include standard Triebel-Lizorkin spaces $F^s_{p,q} (\Omega)$ and hence classical $L_p$-Sobolev spaces $H^s_p(\Omega)$. Key words: Triebel-Lizorkin-Morrey space, Morrey space, Lipschitz domain, oscillations, higher order differences

翻译：本文研究定义在（特殊或有界）Lipschitz域$\Omega\subset\mathbb{R}^d$及$\mathbb{R}^d$上的正光滑度$s$的Triebel-Lizorkin-Morrey空间$\mathcal{E}^{s}_{u,p,q}(\Omega)$。对于这些空间，我们证明了基于局部振荡的新的等价刻画，该刻画在参数满足某些标准条件时成立。作为副产品，我们还利用高阶差分获得了$\mathcal{E}^{s}_{u,p,q}(\Omega)$的新表征。特例包括标准Triebel-Lizorkin空间$F^s_{p,q} (\Omega)$以及经典$L_p$-Sobolev空间$H^s_p(\Omega)$。关键词：Triebel-Lizorkin-Morrey空间，Morrey空间，Lipschitz域，振荡，高阶差分