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

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.