  We consider the problem of describing the traces of functions in
$H^2(\Omega)$ on the boundary of a Lipschitz domain $\Omega$ of $\mathbb R^N$,
$N\geq 2$. We provide a definition of those spaces, in particular of
$H^{\frac{3}{2}}(\partial\Omega)$, by means of Fourier series associated with
the eigenfunctions of new multi-parameter biharmonic Steklov problems which we
introduce with this specific purpose. These definitions coincide with the
classical ones when the domain is smooth. Our spaces allow to represent in
series the solutions to the biharmonic Dirichlet problem. Moreover, a few
spectral properties of the multi-parameter biharmonic Steklov problems are
considered, as well as explicit examples. Our approach is similar to that
developed by G. Auchmuty for the space $H^1(\Omega)$, based on the classical
second order Steklov problem.
