  Let $D$ be a strictly pseudoconvex domain and $X$ be a singular analytic set
of pure dimension $n-1$ in $C^n$ such that $X\cap D\neq \emptyset$ and $X\cap
bD$ is transverse. We give sufficient conditions for a function holomorphic on
$D\cap X$ to admit a holomorphic extension which belongs to $L^q(D),$ $q\in
[1,+\infty[$, or to $BMO(D)$. The extension is given by mean of integral
representation formulas and residue currents.
