Let $D$ be a smooth, bounded domain. $W^{s,p} (D)$ denotes the fractional Sobolev space defined as in Hitchhiker's Guide to Fractional Sobolev Space. Assume that $s>\frac{1}{p}$. I want to show that there exists an continuous linear transformation $T:W^{s, p} (D) \to L^p(\partial D) $ such that Tu=u on $\partial D$ whenever $u$ is continuous.
There are books/papers where the case $p=2$ is taken care of but I want a proof in this setup. Some authors have cited Théorèmesdetraceetd’interpolation but I could figure out where it is done.
Also, may be for the problem I posed, the proof will become much simpler because I only want to show that the trace operator is continuous ant the codomain is Lebesgue space not a Sobolev space.