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

R. F. Shamoyan

Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 361-371.

Résumé

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 $\lambda_{\alpha}^{(n)}$, $0\alpha\le1$, $n\geq0$.