Abstract:
Using the Riemann-Liouville integration-differentiation operator M. M. Djrbashyan general- ized the class of R. Nevanlinna's meromorphic functions in the unit circle including the product $B_\alpha(-1<\alpha<\infty)$, which in the special case of $\alpha=0$ coincide with the Blaschke product. Furthermore, when $(-1<\alpha<0)$, M. M. Djrbashyan and V. S. Zakaryan showed a connection between the products $B_\alpha$ and B of Blaschke.In this work, using this connection theorem we prove that the infinite product $B_\alpha(-1<\alpha<0)$ doesn't belong to $D^2_0$ - the class of analytic functions in the unit circle with finite Dirichlet integral. This means$B_\alpha$ that the derivative of B doesn't belong to the class $H^1$ .
