What does this notation mean? $ f \in C^0 ([0,1] , W^{3,2} (K) ) $

Question

$$ f \in C^0 ([0,1] , W^{3,2} (K) ) $$

Here $W^{n,m}$ is a Sobolev Space, and K is a subset of $\mathbb R^3$ .

Answer 1

$f$ is a continuous map from the unit interval into the function space $W^{3,2}(K)$.

Edit (after OP made his question more precise):

If $f:[0,\infty)\times \mathbb{R}^3 \rightarrow \mathbb{R}$

then $t\mapsto f(t, .)$ may be viewed as a map from the positive real axis to maps $\mathbb{R}^3 \rightarrow \mathbb{R}$

By restriction (on both arguments), such a map gives rise to a map $[0,1]\rightarrow \{\phi: K\rightarrow \mathbb{R}\}$. Then your notation means that for this restriction the first sentence of my answer applies.