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Let $D$ be a strictly pseudoconvex domain and $X$ be a singular analytic setof pure dimension $n-1$ in $C^n$ such that $X\cap D\neq \emptyset$ and $X\capbD$ 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 integralrepresentation formulas and residue currents.

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