Geodesic
Remark on Zero Sets of Holomorphic Functions in Convex Domains of Finite Type
Canadian mathematical bulletin, Tome 53 (2010) no. 2, pp. 311-320

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DOI

We prove that if the $\left( 1,\,1 \right)$ -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 $\log \,\left| f \right|$ 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.
DOI : 10.4153/CMB-2010-037-3
Mots-clés : 32A60, 32A35, 32F18 
Jasiczak, Michał. Remark on Zero Sets of Holomorphic Functions in Convex Domains of Finite Type. Canadian mathematical bulletin, Tome 53 (2010) no. 2, pp. 311-320. doi: 10.4153/CMB-2010-037-3
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     author = {Jasiczak, Micha{\l}},
     title = {Remark on {Zero} {Sets} of {Holomorphic} {Functions} in {Convex} {Domains} of {Finite} {Type}},
     journal = {Canadian mathematical bulletin},
     pages = {311--320},
     year = {2010},
     volume = {53},
     number = {2},
     doi = {10.4153/CMB-2010-037-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-037-3/}
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