# Question regarding Sobolev embeddings

1. Jan 1, 2012

### phibonacci

Hi,

I'm having a bit of trouble understanding certain Sobolev embedding theorems. For instance, if 1 ≤p<∞, and m,j are non-negative integers and mp>n then Wj+m,p(ℝn) embeds into CjB(ℝn). (See for instance Adams and Fournier, Sobolev Spaces, 2nd edition, Theorem 4.12 p. 85). But does this result mean that every function in Wj+m,p(ℝn) is continuously differentiable in the classical sense up to order j (with the function and its classical derivatives up to order j being bounded and continuous), or does it simply mean that the function has weak derivatives up to order j, and that the function and these weak derivatives are continuous and bounded?