Assuming $Q$ is a bounded domain that's as regular as we would like. I am familiar with quite a few trace results, such as the trace embedding $W^{l,p}(Q) \hookrightarrow W^{\bar{l}, p}(\partial Q)$, as is the compactness of that embedding for $\bar{l} < l-1/p$, as well as some results on trace embedding for anisotropic spaces, but none related to the compactness of the trace embedding in the anisotropic space.
In addition to the texts where one might expect to find such a result (e.g. Ladyzhenskaya, Solonnikov, & Ural'ceva: Linear and Quasilinear Parabolic Equations), I have looked to Grisvard's Elliptic Equations in Nonsmooth Domains without much luck. This case doesn't seem to be treated in Besov, Ilin, & Nikolskii's text on function spaces either, but I'll admit to not having read some of the largest (but most dense) function space books in case anyone has a pointer.
Is anyone aware of references towards trace results of the form $$ W^{l_1, l_2, \ldots, l_n, p}(Q) \hookrightarrow W^{\bar{l}_1, \bar{l}_2, \ldots, \bar{l}_n, q}(\partial Q) $$
(I'll be happy with results in a Besov or Sobolev-Slobodeckii sense, and any special cases, so long as they're anisotropic)
Thanks in advance for any help!