H\"older regularity of the $\bar\partial-$equation on the polydisc

Abstract

In this note, we show the existence of a solution operator to the $\bar\partial-$equation in the polydisc that preserves H\"older regularity. This solution operator is constructed using Henkin's formula. It is a well-known fact that solution operators to the $\bar\partial-$equation on product domains do not improve H\"older regularity. Hence, this solution operator is optimal in that regard.