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 $\beta \in (\frac{1}{2};\frac{3}{2})$ a complete description of the spaces of Borel transforms of functions from $P_{\beta }(D)$ is given.