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

TL;DR

This paper solves the open problem of establishing sharp constants in the Paley problem for plurisubharmonic functions of lower order greater than one, extending previous results limited to order up to one.

Contribution

It provides the first sharp estimates for the Paley problem when the lower order exceeds one, advancing the understanding of plurisubharmonic functions of higher order.

Findings

Established sharp constants for $ ho>1$ in Paley problem

Provided estimates for characteristic functions $T(r,u)$ and $M(r,u)$

Extended previous results from $ ho o 1$ to $ ho>1$

Abstract

In 1999 Khabibullin established the best estimate in Paley problem for a plurisubharmonic function $u$ of finite lower order $0\leq\rho\leq 1$. 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 $M(r,u)$.