Hölder estimates on lineally convex domains of finite type (Q874433)

Let \(D\) be a lineally convex domain in \(\mathbb C^n\) with \(C^{\infty}\)-smooth boundary of finite type \(m.\) \(C^0_{(0,q)} (\overline D)\) is the Banach space of \((0,q)\)-forms with continuous coefficients on \(\overline D\) and \(\Lambda^{1/m}_{(0,q)} (D) \) is the Banach space of \((0,q)\)-forms with coefficients that are uniformly Hölder continuous of order \(1/m\) on \(D.\) The authors establish the existence of bounded linear operators \[ T_q: C^0_{(0,q)} (\overline D) \to \Lambda^{1/m}_{(0,q)} (D) \] such that \(\overline \partial T_q f = f \) for all \(f \in C^0_{(0,q)} (\overline D), \overline \partial f = 0.\) For these operators they obtain a nonisotropic Hölder estimate.