Zero varieties for the Nevanlinna class on all convex domains of finite type
Copyright policy )Zero varieties for the Nevanlinna class on all convex domains of finite type
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.
- University of Wuppertal Germany
- Département de Mathématiques France
32W05, Zero sets of holomorphic functions of several complex variables, 32F32, convex domain of finite type, 32A22, \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables, Nevanlinna class, Blaschke condition, Analytical consequences of geometric convexity (vanishing theorems, etc.), 32T25, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, \(\overline\partial\)-Neumann operator
32W05, Zero sets of holomorphic functions of several complex variables, 32F32, convex domain of finite type, 32A22, \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables, Nevanlinna class, Blaschke condition, Analytical consequences of geometric convexity (vanishing theorems, etc.), 32T25, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, \(\overline\partial\)-Neumann operator
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