Borel transforms of functions from a parameterized family of Hilbert spaces of entire functions

We introduce a continuous scale of Hilbert spaces of entire functions $P_\beta (D)$ for a bounded convex domain $D$ on the complex plane. For the parameters $\beta \in (\frac 12;\frac 32)$ a complete description of the spaces of Borel transforms of functions from $P_\beta (D)$ is given.