Let ω be a C²-smooth strictly pseudoconvex domain in C n, let A(ω) denote the class of functions holomorphic in the interior {Mathematical expression} and continuous in ω, let P(ω) be the closure of holomorphic polynomials in the uniform C(ω)-norm, and let {Mathematical expression} be the Hölder class of holomorphic functions. With the assumption P(ω)=A(ω) a theorem concerning Λ^α(Ω) analogous to the classical Jackson-Bernstein theorem is proved.