Compact immersions of the bounded variation space $BV(\Omega)$

Question

I have missed a detail attending a lesson, I would like at least some references to fill my gap. We were proving the compact immersion of $BV(\Omega)$ in $L^p(\Omega)$ with $1\leq p<1^{*}$ and $\Omega$ an open regular bounded set of $\mathbb{R}^N$. We had already proved $BV(\Omega) \hookrightarrow L^1(\Omega)$ compactly and that $BV(\Omega)\hookrightarrow L^{1*}(\Omega)$ continuously, here comes the detail I missed, so by interpolation we concluded $BV(\Omega) \hookrightarrow L^p(\Omega)$ compactly for $1\leq p<1^{*}$. What did the professor meant by interpolation? I thought he was referring to the Marcinkiewicz's theorem, but in the statement of the theorem I did not found any reference to compact operators but only bounded ones. Hope I have been clear, thanks for the attention