T. Nguyen

$L^p$ Estimates for the $\bar{\partial}$-Problem on Rational Hartogs Triangles

We investigate $L^p$ estimates for the $\bar{\partial}$-problem on rational Hartogs triangles $\mathbb{H}_{m/n} = \{ (z_1, z_2) \in \mathbb{C}^2 : |z_1|^m<|z_2|^n<1 \}$. For $p \in (1, \infty)$, we establish the existence of a solution operator that is bounded on $L^p(\mathbb{H}_{m/n})$. Our approach avoid the need for...