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Zero varieties for the Nevanlinna class on all convex domains of finite type

Published online by Cambridge University Press:  22 January 2016

Klas Diederich  and
Emmanuel Mazzilli
Klas Diederich
Affiliation:
Mathematik, Universitä Wuppertal, Gausstr. 20, D-42097 Wuppertal, Germany, klas@uni-wuppertal.de
Emmanuel Mazzilli
Affiliation:
Département de Mathématiques, CNRS URA D751, Université Lille 1, F-59655 Villeneuve d’Ascq, France, emmanuel.mazzilli@agat.univ-lille1.fr
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Abstract

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It is shown, that the so-called Blaschke condition characterizes in any bounded smooth convex domain of finite type exactly the divisors which are zero sets of functions of the Nevanlinna class on the domain. The main tool is a non-isotropic L1 estimate for solutions of the Cauchy-Riemann equations on such domains, which are obtained by estimating suitable kernels of Berndtsson-Andersson type.

Keywords

32A3532A2632A6032F3232F4532W05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 163 , September 2001 , pp. 215 - 227
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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