Uncertainty inequality on weighted Hardy spaces.

In this paper we introduce a weighted Hardy space ℋ β . This space generalizes some complex Hilbert spaces like the Dirichlet space 풟 , the Bergman space 풜 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 β on ℋ β . Furthermore, we establish a general uncertainty inequality of Heisenberg type for the space ℋ β . [ABSTRACT FROM AUTHOR]