Paley problem for plurisubharmonic functions of finite lower order

For plurisubharmonic functions $\mathbb C^n$ of lower order $\lambda<+\infty$ estimates of the growth of their maximum value on the sphere of radius $r$ with centre at the origin in terms of the growth of the Nevanlinna characteristics $T(r,u)$ are obtained. These estimates are best possible for $\lambda\leqslant 1$. The results are new even in the case of functions of the form $u=\log|f|$, where $f$ is an entire function in $\mathbb C^n$, $n>1$.