Let Ω⊂ Cⁿ be a strictly pseudoconvex Runge domain with C²-smooth defining function, l∈ N, p∈ (1 , ∞). We prove that a holomorphic function f has derivatives of order l in H^p(Ω) if and only if there is a sequence {P2k} such that P2k is a polynomial of degree 2 ^k and ∑k=1∞22lk|f(z)-P2k(z)|2∈Lp(∂Ω).