UNCERTAINTY INEQUALITIES FOR WEIGHTED SPACES OF ANALYTIC FUNCTIONS ON THE UNIT DISK

In this paper we establish uncertainty inequality of Heisenberg type for Hardy space H, Dirichlet space D and Bergman space B, respectively. Next, we introduce a weighted Hardy space H-beta. This space which gives a generalization of some Hilbert spaces of analytic functions on the unit disk like, the Hardy space H, the Dirichlet space D and the Bergman space B, it plays a background to our contribution. Especially, we study the derivative operator D and its adjoint operator L. on H-beta, and we deduce a general uncertainty inequality of Heisenberg type for this space.