Is $L^p$ for $p \in [1, \frac{N}{N-1}$ continuously embedded in $L^1$?

Question

Let $\Omega$ be an open bounded subset of $\mathbb{R}^N$ for $N \geq 2$.

Is the space $L^p(\Omega)$ for $p \in [1, \frac{N}{N-1})$ continuously embedded in $L^1(\Omega)$?

I need this property for a proof to apply Aubin-Lions Lemma.q