Bounds for (k,c) model functions over p-adic fields

Let $F$ be a $p$-adic field, let $k,c\ge1$, and let $ρ$ be a $(k,c)$ representation of $\mathrm{GL}_{kc}(F)$: a complex representation of finite length whose wave front set has $(k^c)$ as its unique maximal orbit, and which admits a $(k,c)$ functional that is unique up to scaling. We prove that the