On Extension Properties of Pluricomplex Green Functions
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 2, pp. 329-356.

À condition que Ω 0 est une domaine bornée dans n et soit compact sous-ensemble de Ω 0 en maintenant que Ω:=Ω 0 soit connexe, cet article va examiner les propriétés d’extension de la fonction de Green pluricomplexe de Ω en sous-domaines strictement plus larges Ω ˜ de Ω comme une fonction de Green pluricomplexe. Le problème sera examiné quand Ω 0 soit une domaine Reinhardt complète bornée pseduconvexe dans n et une étude détaillée sur unité disque Δ 2 2 sera fournie.

Let Ω 0 be a bounded domain in n and be a compact subset of Ω 0 such that Ω:=Ω 0 is connected. This paper deals with the study of the extension properties of the pluricomplex Green function of Ω to strictly larger subdomains Ω ˜ of Ω as a pluricomplex Green function. The problem will be studied when Ω 0 is a pseudoconvex, bounded complete Reinhardt domain in n and a detailed study in unit bidisc Δ 2 2 will be provided.

Reçu le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/afst.1601
Classification : 32U35
Mots clés : pluricomplex Green functions, convex functions, Reinhardt domains
@article{AFST_2019_6_28_2_329_0,
     author = {Kur\c{s}ung\"oz, S. Zeynep \"Ozal},
     title = {On {Extension} {Properties} of {Pluricomplex} {Green} {Functions}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {329--356},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {2},
     year = {2019},
     doi = {10.5802/afst.1601},
     mrnumber = {3957683},
     zbl = {07095684},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/afst.1601/}
}
TY  - JOUR
AU  - Kurşungöz, S. Zeynep Özal
TI  - On Extension Properties of Pluricomplex Green Functions
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2019
DA  - 2019///
SP  - 329
EP  - 356
VL  - Ser. 6, 28
IS  - 2
PB  - Université Paul Sabatier, Toulouse
UR  - http://archive.numdam.org/articles/10.5802/afst.1601/
UR  - https://www.ams.org/mathscinet-getitem?mr=3957683
UR  - https://zbmath.org/?q=an%3A07095684
UR  - https://doi.org/10.5802/afst.1601
DO  - 10.5802/afst.1601
LA  - en
ID  - AFST_2019_6_28_2_329_0
ER  - 
Kurşungöz, S. Zeynep Özal. On Extension Properties of Pluricomplex Green Functions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 2, pp. 329-356. doi : 10.5802/afst.1601. http://archive.numdam.org/articles/10.5802/afst.1601/

[1] Bedford, Eric; Burns, Dan Domains of existence for plurisubharmonic functions, Math. Ann., Volume 238 (1978) no. 1, pp. 67-69 | MR 510308 | Zbl 0403.32011

[2] Cegrell, Urban On the domains of existence for plurisubharmonic functions, Complex analysis (Warsaw, 1979) (Banach Center Publications), Volume 11, PWN - Polish Scientific Publishers, 1983, pp. 33-37 | MR 737748 | Zbl 0539.32012

[3] Cegrell, Urban Plurisubharmonic functions outside compact sets, Proc. Am. Math. Soc., Volume 103 (1988) no. 1, pp. 81-84 | MR 938648 | Zbl 0654.32009

[4] Harvey, Reese; Polking, John Extending analytic objects, Commun. Pure Appl. Math., Volume 28 (1975) no. 6, pp. 701-727 | MR 409890 | Zbl 0323.32013

[5] Jarnicki, Marek; Pflug, Peter First steps in several complex variables: Reinhardt domains, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2008 | Zbl 1148.32001

[6] Klimek, Maciej Extremal plurisubharmonic functions and invariant pseudodistances, Bull. Soc. Math. Fr., Volume 113 (1985) no. 2, pp. 231-240 | MR 820321 | Zbl 0584.32037

[7] Klimek, Maciej Invariant pluricomplex Green functions, Topics in complex analysis (Warsaw, 1992) (Banach Center Publications), Volume 31, PWN - Polish Scientific Publishers, 1995, pp. 207-226 | MR 1341390 | Zbl 0844.31004

[8] Sadullaev, S. Extension of plurisubharmonic functions from a submanifold (Russian), Dokl. Akad. Nauk UzSSR (1982), pp. 3-4 | MR 668967 | Zbl 0637.32014

[9] Yan, Min Extension of convex function, J. Convex Anal., Volume 21 (2014) no. 4, pp. 965-987 | MR 3331205 | Zbl 1312.26027

[10] Zakharyuta, V. P. Spaces of analytic functions and maximal plurisubharmonic functions (Russian), D. Sc. Dissertation, Rostov-on-Don, 1984

Cité par Sources :