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We construct homotopy formulas for $\overline\partial$-equations on convexdomains of finite type that have optimal Sobolev and H\"older estimates. For abounded smooth finite type convex domain $\Omega\subset\mathbb C^n$ that has$q$-type $m_q$ for $1\le q\le n$, our $\overline\partial$ solution operator$\mathcal T_q$ on $(0,q)$-forms has (fractional) Sobolev boundedness $\mathcalT_q:H^{s,p}\to H^{s+1/m_q,p}$ and H\"older-Zygmund boundedness $\mathcalT_q:\mathscr C^s\to\mathscr C^{s+1/m_q}$ for all $s\in\mathbb R$ and$1<p<\infty$. We also show the $L^p$-boundedness $\mathcal T_q:H^{s,p}\toH^{s,pr_q/(r_q-p)}$ for all $s\in\mathbb R$ and $1<p<r_q$, where$r_q:=(n-q+1)m_q+2q$.

Sobolev and H\"older Estimates for Homotopy Operators of $\overline\partial$-Equations on Convex Domains of Finite Multitype