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The space $F^p$ ($1<p<\infty$) consists of all holomorphic functions $f$ onthe open unit disk $\Bbb D$ for which $\lim_{r\to1}(1-r)^{1/q}\log^+M_{\infty}(r,f)=0,$ where $M_{\infty}(r,f)=\max_{\vertz\vert\le r}\vert f(z)\vert$ with $0<r<1$. Stoll [5, Theorem 3.2] proved thatthe 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 $\Vertf\Vert_{q,c}:=\sum_{n=0}^{\infty}\vert a_n\vert\exp\left(-cn^{1/(q+1)}\right)<\infty,$ is a countably normed Fr\'{e}chet algebra. Notice that foreach $p>1$, $F^p$ is the Fr\'{e}chet envelope of the Privalov space $N^p$. Inthis paper we study the structure of maximal ideals in the algebras $F^p$($1<p<\infty$). In particular, we give a complete characterization of closedmaximal ideals in $F^p$. Moreover, we characterize multiplicative linearfunctionals on $F^p$.

A characterization of maximal ideals in the Fr\'{e}chet algebras of holomorphic functions $F^p$ $(1