Hölder estimates on convex domains of finite type
نویسندگان
چکیده
This article contains a natural and important application of the holomorphic support functions for convex domains of finite type in Cn constructed in [DiFo]. Namely, we use these functions to get ∂-solving Cauchy-Fantappié kernels for ∂-closed (0, q)-forms, such that the solutions given by them on bounded forms satisfy the best possible uniform Hölder estimates. More precisely we show: Theorem 1.1 Let D ⊂⊂ Cn be a linearly convex domain with C∞-smooth boundary of finite type m. We denote by L(0,q)(D) the Banach space of (0, q)-forms with bounded coefficients on D and by Λ (0,q)(D) the Banach space of (0, q)-forms whose coefficients are uniformly Hölder continuous of order 1/m on D. Then there are bounded linear operators
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تاریخ انتشار 1999