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1. CMB 2010 (vol 53 pp. 311)

Jasiczak, MichaƂ
Remark on Zero Sets of Holomorphic Functions in Convex Domains of Finite Type
We prove that if the $(1,1)$-current of integration on an analytic subvariety $V\subset D$ satisfies the uniform Blaschke condition, then $V$ is the zero set of a holomorphic function $f$ such that $\log |f|$ is a function of bounded mean oscillation in $bD$. The domain $D$ is assumed to be smoothly bounded and of finite d'Angelo type. The proof amounts to non-isotropic estimates for a solution to the $\overline{\partial}$-equation for Carleson measures.

Categories:32A60, 32A35, 32F18

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