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The purpose of this paper is to characterize the zero sets of holomorphicfunctions in the Nevanlinna class on a class of convex domains of infinite typein $\mathbb{C}^2$. Moreover, we also obtain $L^p$ estimates, $1 \leq p \leq\infty$, for a particular solution of the tangential Cauchy-Riemann equation onthe boundaries of these domains.

Zero sets of functions in the Nevanlinna class and the $\bar\partial_b$-equation on convex domains of general type in $\mathbb{C}^2$