A representation of linear functionals on some class of holomorphic functions in the unit disk

A description is given for the dual space to the class of holomorphic functions in $\mathbb D=\{z:|z|<1\}$ such that $\lim\limits_{r\to 1-0}\frac{(1-r)^2}{\omega(1-r)}D^{\alpha+2}(f(re^{i\varphi}))=0$, uniformly in $\varphi$, $\omega(\delta)$ being a function of modulus of continuity type, $\alpha\geq0$. The result extends a known Duren–Romberg–Shields theorem on the dual space to the class $\lambda_{\alpha}^{(n)}$, $0<\alpha\le1$, $n\geq0$.