Paley problem for plurisubharmonic functions of lower order $\rho \gt 1$
Volume 289 / 2026
Studia Mathematica 289 (2026), 53-77
MSC: Primary 31B05; Secondary 32U05, 26D10 42B25
DOI: 10.4064/sm250422-31-7
Published online: 15 June 2026
Abstract
Khabibullin established the best estimate in the Paley problem for a plurisubharmonic (psh) function $u$ of lower order, $0\leq \rho \leq 1$. For $\rho \gt 1$, obtaining a sharp estimate has remained an open question. In this work, we solve this problem. We also provide estimates for the types of characteristic functions $T(r,u)$ and $M(r,u)$. Finally, we compare our results with those of Dahlberg for subharmonic functions and show that the latter are not optimal for psh functions of finite lower order $\rho \gt 1$.
