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

TL;DR

This paper characterizes zero sets of Nevanlinna class functions on convex domains of infinite type in ^2 and provides L^p estimates for solutions to the _b-equation on their boundaries.

Contribution

It offers a characterization of zero sets in the Nevanlinna class and establishes L^p estimates for solutions to the _b-equation on these complex domains.

Findings

Characterization of zero sets in the Nevanlinna class.

L^p estimates for solutions of the _b-equation.

Results applicable to convex domains of infinite type in ^2.

Abstract

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