Constructive description of Hardy-Sobolev spaces in strictly pseudoconvex domains with minimal smoothness

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