On Sharp Constants for Dual Segal--Bargmann $L^p$ Spaces

William E. Gryc, Todd Kemp

We study dilated holomorphic $L^p$ space of Gaussian measures over ${\mathbb{C}}^n$, denoted ${\mathcal{H}}_{p,\alpha }^n$ with variance scaling parameter $\alpha >0$. The duality relations $(\mat…