If $ u \in W^{2,3} ( \Omega ) $ then $u \in L^3 ( \Omega )$?

Question

If $ u \in W^{2,3} ( \Omega ) $ then $u \in L^3 ( \Omega )$ ?

In wikipedia, the definition of Sobolev space is $$ W^{k,p} ( \Omega) = \{ u \in L^p ( \Omega)\mid D^{\alpha} u \in L^p , | \alpha| \leqslant k \},$$ where $ \Omega $ is an open set in $\mathbb R^n$. So I think it's trivial, is this right?

Answer 1

The set-builder notation you see causes $W^{k,p}(\Omega)$ to consist of functions in $L^p(\Omega)$.