  We propose here to garnish the folklore of function spaces on Lipschitz
domains. We prove the boundedness of the trace operator for homogeneous Sobolev
and Besov spaces on a special Lipschitz domain with sharp regularity. In order
to obtain such a result, we also provide appropriate definitions and properties
so that our construction of homogeneous of Sobolev and Besov spaces on special
Lipschitz domains, and their boundary, that are suitable for the treatment of
non-linear partial differential equations and boundary value problems. The
trace theorem for homogeneous Sobolev and Besov spaces on special Lipschitz
domains occurs in range $s\in(\frac{1}{p},1+\frac{1}{p})$. While the case of
inhomogeneous Sobolev and Besov spaces is very common and well known, the case
of homogeneous function spaces seems to be new. This paper uses and improves
several arguments exposed by the author in a previous paper for function spaces
on the whole and the half-space.
