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

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