Let $G=GL_n(F)$, where $F$ is a p-adic local field, $U$ be the maximal upper triangular unipotent group, and $\theta$ a character of $U$. Then a Theorem of Kazhdan says that for any irreducible smooth representation $(\pi,V)$ of $G$, we have $$\dim V_{U,\theta} $$ has finite dimension, where $V_{U,\theta}$ is the twisted Jacquet functor. This is Theorem 5.21 of "Bernstein-Zelevinski, Representations of $GL(n,F)$, where $F$ is a non-archimedean local field". In fact, in Theorem 5.21, the above dimension is bounded by $n!$.

My question is: is this theorem true for more general groups?  If it is, where can I find a proof?

Thanks.