2023/01/11 by Loo, Yu Jun, Tumanov, Alexander
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2301.04484
In this note, we show the existence of a solution operator to the ∂-equation in the polydisc that preserves Hölder regularity. This solution operator is constructed using Henkin's formula. It is a well-known fact that solution operators to the ∂-equation on product domains do not improve Hölder regularity. Hence, this solution operator is optimal in that regard.