  The critical behaviour of $d$-dimensional semi-infinite systems with
$n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk
Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional
subspace of $\mathbb{R}^d$. Field-theoretic renormalization group methods are
utilised to examine the special surface transition in the case where the $m$
potential modulation axes, with $0\leq m\leq d-1$, are parallel to the surface.
The resulting scaling laws for the surface critical indices are given. The
surface critical exponent $\eta_\|^{\rm sp}$, the surface crossover exponent
$\Phi$ and related ones are determined to first order in
$\epsilon=4+\case{m}{2}-d$. Unlike the bulk critical exponents and the surface
critical exponents of the ordinary transition, $\Phi$ is $m$-dependent already
at first order in $\epsilon$. The $\Or(\epsilon)$ term of $\eta_\|^{\rm sp}$ is
found to vanish, which implies that the difference of $\beta_1^{\rm sp}$ and
the bulk exponent $\beta$ is of order $\epsilon^2$.
