Optimal Sobolev regularity of $\bar{\partial }$ on the Hartogs triangle

Abstract

In this paper, we show that for each $k\in {\mathbb{Z}}^{+},p>4$, there exists a solution operator ${\mathcal{T}}_k$ to the $\bar{\partial }$ problem on the Hartogs triangle that maintains the same $W^{k,p}$ regularity as that of the data. According to a Kerzman-type example, this operator provides solutions with the optimal Sobolev regularity.

23 pages