The Cauchy-Riemann Equations in Convex Domains

1991 ◽  
pp. 247-253
Author(s):  
John C. Polking
Keyword(s):  
Convex Domains ◽  
Cauchy Riemann

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

2001 ◽  
Vol 163 ◽  
pp. 215-227 ◽  
Author(s):  
Klas Diederich ◽  
Emmanuel Mazzilli
Keyword(s):  
Finite Type ◽  
Convex Domain ◽  
Main Tool ◽  
Smooth Convex ◽  
Convex Domains ◽  
Zero Sets ◽  
Nevanlinna Class ◽  
Cauchy Riemann ◽  
Bounded Smooth

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.

SOME BOUNDARY VALUE PROBLEMS FOR THE CAUCHY-RIEMANN EQUATION IN HALF LENS

2018 ◽  
Vol 9 (3) ◽  
pp. 73-84
Author(s):  
N. Taghizadeh ◽  
◽  
V. Soltani Mohammadi ◽  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Riemann Equation ◽  
Cauchy Riemann
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