  The space $F^p$ ($1<p<\infty$) consists of all holomorphic functions $f$ on
the open unit disk $\Bbb D$ such that $ \lim_{r\to
1}(1-r)^{1/q}\log^+M_{\infty}(r,f)=0,$ where $M_{\infty}(r,f)=\max_{\vert
z\vert\le r}\vert f(z)\vert$ with $0<r<1$. Stoll [5, Theorem 3.2] proved that
the space $F^p$ with the topology given by the family of seminorms
$\left\{\Vert \cdot\Vert_{q,c}\right\}_{c>0}$ defined for $f\in F^q$ as $\Vert
f\Vert_{q,c}:=\sum_{n=0}^{\infty}\vert a_n\vert\exp\left(-cn^{1/(q+1)}
\right)<\infty$, becomes a countably normed Fr\'{e}chet algebra. It is known
that for every $p>1$, $F^p$ is the Fr\'{e}chet envelope of the Privalov space
$N^p$. In this paper, we extend our study of [32] on the structure of maximal
ideals in the algebras $F^p$ ($1<p<\infty$). Namely, the obtained
characterization of closed maximal ideals in $F^p$ from [32] is extended here
in terms of topology of uniform convergence on compact subsets of $\Bbb D$.
