Zero Varieties for the Nevanlinna Class in Convex Domains of Finite Type in \Bbb C n

1998 ◽  
Vol 147 (2) ◽  
pp. 391 ◽  
Author(s):  
Joaquim Bruna ◽  
Philippe Charpentier ◽  
Yves Dupain
Keyword(s):  
Finite Type ◽  
Convex Domains ◽  
Nevanlinna Class

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.

Ck-estimates for the -equation on convex domains of finite type

2005 ◽  
Vol 252 (3) ◽  
pp. 473-496 ◽  
Author(s):  
William Alexandre
Keyword(s):  
Finite Type ◽  
Convex Domains

scholarly journals Gain of Regularity in Extension Problem on Convex Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Jasiczak
Keyword(s):  
Finite Type ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Extension Problem ◽  
Convex Domains

We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constantdsuch that on Bergman spacesHp(D)with1≤p<dthere appears the so-called “gain regularity.” The constantddepends on the minimum of the dimension and the codimension of the subvariety. This means that the space of functions which admit an extension to a function in the Bergman spaceHp(D)is strictly larger thanHp(D∩A), whereAis a subvariety.

scholarly journals Weighted Lipschitz estimates for ∂¯ on convex domains of finite type

2010 ◽  
Vol 368 (1) ◽  
pp. 190-210
Author(s):  
Jisoo Byun ◽  
Hong Rae Cho ◽  
Jong-Do Park
Keyword(s):  
Finite Type ◽  
Convex Domains ◽  
Lipschitz Estimates
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