My question is about the following compact embedding:
\begin{equation}
C^{\sigma+2, \sigma/2+1}_{x, t}(Q_T)\hookrightarrow C^{\sigma, \sigma/2}_{x, t}(Q_T).
\end{equation}
what condition should be put on $Q_T=\Omega \times (0, T)$ where $\Omega\subset \mathbb{R}$ be an open bounded interval and $T<\infty$, so that the above relation is correct? If this relation is correct, please give me a valid reference. 

We denote by $C^{m+\alpha, \beta}_{x, t}(Q_T)$ ($m$ integer $\geq 0$, $0<\alpha, \beta <1$) the space of function $u(x, t)$ with finite norm 
\begin{equation}
\Vert u \Vert_{C^{m+\alpha, \beta}_{x, t}(Q_T)}=\sum_{\vert l \vert=0}^{m} \Big[ \sup _{Q_T}\vert D^{l}_{x}u \vert +\langle D^{l}_{x}u \rangle^{(\alpha)}_{x, Q_T}+\langle D^{l}_{x}u \rangle^{(\beta)}_{t, Q_T}\Big]
\end{equation}
where
\begin{equation}
\langle w \rangle^{(\alpha)}_{x, Q_T}=\sup_{(x, t), (y, t)\in {Q_T}} \frac {\vert w(x, t)-w(y, t)\vert}{\vert x-y \vert^\alpha},
\end{equation}
\begin{equation}
\langle w \rangle^{(\beta)}_{t, Q_T}=\sup_{(x, t), (x, \tau)\in {Q_T}} \frac {\vert w(x, t)-w(x, \tau)\vert}{\vert t-\tau \vert^\beta}.
\end{equation}
We denote by $C^{\alpha+2, \beta+1}_{x, t}(Q_T)$ the space of functions $u(x, t)$ with norm
\begin{equation}
\Vert u \Vert_{C^{\alpha+2, \beta}_{x, t}(Q_T)}+\Vert u_t \Vert_{C^{\alpha, \beta}_{x, t}(Q_T)}.
\end{equation}