Hölder estimates on convex domains of finite type (Q1307010)

Let \(D\Subset\mathbb{C}^n\) be a linearly convex domain with \({\mathcal C}^\infty\)-smooth boundary of finite type \(m\). We construct bounded \(\overline \partial\)-solving integral kernels \(T_q:L^\infty_{(0,q+1)} (D)\to \Lambda^{1/ m}_{(0,q)} (D)\) from the space of bounded \((0,q+1)\)-forms on \(D\) to the space of uniformly Hölder continuous \((0,q)\)-forms of exponent \({1\over m}\) on \(D\). The main tool are the holomorphic support functions for such domains as constructed recently by \textit{K. Diederich} and \textit{J. E. Fornæss} in Math. Z. 230, No. 1, 145-164 (1999).