  In this paper we prove the Sobolev embeddings for Herz-type Triebel-Lizorkin
spaces, \begin{equation*} \dot{K}_{q}^{\alpha_{2},r}F_{\theta
}^{s_{2}}\hookrightarrow \dot{K}%_{s}^{\alpha_{1},p}F_{\beta }^{s_{1}}
\end{equation*} where the parameters
$\alpha_{1},\alpha_{2},s_{1},s_{2},s,q,r,p,\beta $ and $\theta $ satisfy some
suitable conditions. An application we obtain new embeddings between Herz and
Triebel-Lizorkin spaces. Moreover, we present the Sobolev embeddings for
Triebel-Lizorkin spaces equipped with power weights. All these results cover
the results on classical Triebel-Lizorkin spaces.
