Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates in strictly pseudoconvex domains of $C^n$

Let $D$ be a strictly pseudoconvex domain and $X$ be a singular analytic set of pure dimension $n-1$ in $C^n$ such that $X\cap D\mathrm{\ne }\mathrm{\varnothing }$ and $X\cap bD$istransverse\mathrm{.}Wegivesufficientconditionsforafunctionholomorphicon$D\cap X$toadmitaholomorphicextensionwhichbelongsto$L^q(D),$ $q\in [1,+\infty[$,orto$BMO(D)$. The extension is given by mean of integral representation formulas and residue currents.