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In this paper, we prove weighted $L^p$ estimates for the canonical solutionson product domains. As an application, we show that if $p\in [4, \infty)$, the$\bar\partial$ equation on the Hartogs triangle with $L^p$ data admits $L^p$solutions with the desired estimates. For any $\epsilon>0$, by constructing anexample with $L^p$ data but having no $L^{p+\epsilon}$ solutions, we verify thesharpness of the $L^p$ regularity on the Hartogs triangle.

Optimal $L^p$ regularity for $\bar\partial$ on the Hartogs triangle