Division of holomorphic functions and growth conditions

Alexandre, William; Mazzilli, Emmanuel

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Division of holomorphic functions and growth conditions

Author(s) :

Alexandre, William [Auteur correspondant]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Mazzilli, Emmanuel [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Illinois Journal of Mathematics

Publication date :

2013

English keyword(s) :

Residue currents
Division of holomorphic functions

HAL domain(s) :

Mathématiques [math]/Variables complexes [math.CV]

English abstract : [en]

Let D be a strictly convex domain of C^n, f_1 and f_2 be two holomorphic functions defined on a neighborhood of \overline D and set X_l={z, f_l(z)=0}, l=1,2. Suppose that X_l\cap bD is transverse for l=1 and l=2, and that ...
Show more >Let D be a strictly convex domain of C^n, f_1 and f_2 be two holomorphic functions defined on a neighborhood of \overline D and set X_l={z, f_l(z)=0}, l=1,2. Suppose that X_l\cap bD is transverse for l=1 and l=2, and that X_1\cap X_2 is a complete intersection. We give necessary conditions when n\geq 2 and sufficient conditions when n=2 under which a function g can be written as g=g_1f_1+g_2f_2 with g_1 and g_2 in L^q(D), q\in [1,+\infty), or g_1 and g_2 in BMO(D). In order to prove the sufficient condition, we explicitly write down the functions g_1 and g_2 using integral representation formulas and new residue currents.Show less >

Language :

Anglais

Popular science :

Non

Comment :

30 pages

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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