  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.
