location:  Publications → journals → CMB
Abstract view

# Remark on Zero Sets of Holomorphic Functions in Convex Domains of Finite Type

Published:2010-04-06
Printed: Jun 2010
• Michał Jasiczak,
Faculty of Mathematics and Computer Science, A. Mickiewicz University, 61-614 Poznan, Poland and
Institute of Mathematics, Polish Academy of Sciences, 00-956 Warsaw, Poland
 Format: HTML LaTeX MathJax

## Abstract

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.
 MSC Classifications: 32A60 - Zero sets of holomorphic functions 32A35 - $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15] 32F18 - Finite-type conditions

 top of page | contact us | privacy | site map |