  We study the validity of (q,p)-Poincar\'e inequalities, q<p, on domains in
R^n which satisfy a quasihyperbolic boundary condition, i.e. domains whose
quasihyperbolic metric satisfies a logarithmic growth condition. In the present
paper, we show that the quasihyperbolic boundary condition domains support a
(q,p)-Poincar\'e inequality whenever p>p_0, where p_0 is an explicit constant
depending on q, on the logarithmic growth condition, and on the boundary of the
domain.
