On sharp constants in Paley problem for plurisubharmonic functions of lower order $\rho >1$

Abstract

In 1999 Khabibullin established the best estimate in Paley problem for a plurisubharmonic function $u$ of finite lower order $0\le \rho \le 1$. For $\rho >1$ obtaining a sharp estimate has remained an open question. In this work we solve this problem. We also provide some estimates for the types of the characteristic functions $T(r,u)$ and $M(r,u)$.