C~k-Estimates for the partial deriv _b-Equation on Convex Domains of Finite Type

摘要

Since the construction in [8] of a support function for convex domains of finite type, many results about the regularity of Cauchy-Riemann equations have been obtained on these domains. We should mention, in which a partial deriv-solving operator for all convex domains of finite type was constructed that satisfies optimal uniform Hoelder estimates. Note that this result was already obtained in [5] by using properties of the Bergman kernel. For a convex domain of finite type, Hefer obtained Hoelder and L~p-estimates depending on Catlin's multitype. In [2], a modification of the operator of [7] led to C~k-estimates for all k ∈ N. In this work, we are interested in the regularity of tangential Cauchy-Riemann equations.