Optimal $$L^p$$ Regularity for $$\bar{\partial }$$ on the Hartogs Triangle

In this paper, we prove weighted \(L^p\) estimates for the canonical solutions on 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 an example with \(L^p\) data but having no \(L^{p+\epsilon }\) solutions, we verify the sharpness of the \(L^p\) regularity on the Hartogs triangle.