Uncertainty inequality on weighted Hardy spaces

In this paper we introduce a weighted Hardy spaceH ss. This space generalizes some complex Hilbert spaces like the Dirichlet space D, the Bergman space A and the Segal-Bargmann space F. It plays the role of background for our contribution. In particular, we study the derivative operator D and its adjoint operator L ss onH ss. Furthermore, we establish a general uncertainty inequality of Heisenberg type for the spaceH ss.