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

Tran Vu Khanh; Andrew Raich

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arXiv · 1605.06985

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

Tran Vu Khanh·Andrew Raich

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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.

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Tran Vu Khanh, Andrew Raich. 2016-05-23. Zero sets of functions in the Nevanlinna class and the $\bar\partial_b$-equation on convex domains of general type in $\mathbb{C}^2$. https://arxiv.org/abs/1605.06985

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