  Let $\Omega\subset\mathbb{C}^n$ be a strictly pseudoconvex Runge domain with
$C^2$-smooth defining function, $l\in\mathbb{N},$ $p\in(1,\infty).$ We prove
that the holomorphic function $f$ has derivatives of order $l$ in $H^p(\Omega)$
if and only if there exists a sequence on polynomials $P_n$ of degree $n$ such
that $\sum\limits_{k=1}^{\infty}2^{2lk}\left\lvert f(z)-P_{2^k}(z)
\right\rvert^2\in L^p(\partial\Omega).$
