A Pointwise Bound for a Holomorphic Function which is Square-Integrable with Respect to an Exponential Density Function

Kamthorn Chailuek, Wicharn Lewkeeratiyutkul

Let $\varphi$ be a real-valued smooth function on $\mathbf{C}$ satisfying $0\le \Delta \varphi \le M$ for some $M\ge 0$. We consider the space of all holomorphic functions which are square-integrab…