Simple view

Full metadata view

Authors

Statistics

-functions in unbounded balanced domains

2017
journal article
article
10.1007/s12220-016-9754-3
Journal
The Journal of Geometric Analysis
35
Author
Pflug Peter

Zwonek Włodzimierz
Volume
27
Issue
3
Pages
2118-2130
ISSN
1050-6926
eISSN
1559-002X
Keywords in English

Balanced domain

Lelong number

Bergman space

-functions

-domain of holomorphy

Language
English
Journal language
English
Abstract in English

We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a description of -domains of holomorphy in the class of balanced domains and present a purely algebraic criterion for homogeneous polynomials to be square integrable in a pseudoconvex balanced domain in . This allows easily to decide which pseudoconvex balanced domain in has a positive Bergman kernel and which admits the Bergman metric.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
Scopus© citations
7
dc.abstract.enWe investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a description of $L_{h}^{2}$-domains of holomorphy in the class of balanced domains and present a purely algebraic criterion for homogeneous polynomials to be square integrable in a pseudoconvex balanced domain in $\mathbb{C}^{2}$. This allows easily to decide which pseudoconvex balanced domain in $\mathbb{C}^{2}$ has a positive Bergman kernel and which admits the Bergman metric.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorPflug, Peterpl
dc.contributor.authorZwonek, Włodzimierz - 132944 pl
dc.date.accessioned2017-07-11T07:01:30Z
dc.date.available2017-07-11T07:01:30Z
dc.date.issued2017pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number3pl
dc.description.physical2118-2130pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume27pl
dc.identifier.doi10.1007/s12220-016-9754-3pl
dc.identifier.eissn1559-002Xpl
dc.identifier.issn1050-6926pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/42598
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 3.0 Polska*
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/pl/legalcode*
dc.share.typeinne
dc.subject.enBalanced domainpl
dc.subject.enLelong numberpl
dc.subject.enBergman spacepl
dc.subject.en$L_{h}^{2}$-functionspl
dc.subject.en$L_{h}^{2}$-domain of holomorphypl
dc.subtypeArticlepl
dc.title$L_{h}^{2}$-functions in unbounded balanced domainspl
dc.title.journalThe Journal of Geometric Analysispl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a description of $L_{h}^{2}$-domains of holomorphy in the class of balanced domains and present a purely algebraic criterion for homogeneous polynomials to be square integrable in a pseudoconvex balanced domain in $\mathbb{C}^{2}$. This allows easily to decide which pseudoconvex balanced domain in $\mathbb{C}^{2}$ has a positive Bergman kernel and which admits the Bergman metric.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Pflug, Peter
dc.contributor.authorpl
Zwonek, Włodzimierz - 132944
dc.date.accessioned
2017-07-11T07:01:30Z
dc.date.available
2017-07-11T07:01:30Z
dc.date.issuedpl
2017
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.numberpl
3
dc.description.physicalpl
2118-2130
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
27
dc.identifier.doipl
10.1007/s12220-016-9754-3
dc.identifier.eissnpl
1559-002X
dc.identifier.issnpl
1050-6926
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/42598
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Udzielam licencji. Uznanie autorstwa 3.0 Polska
dc.rights.licence
CC-BY
dc.rights.uri*
http://creativecommons.org/licenses/by/3.0/pl/legalcode
dc.share.type
inne
dc.subject.enpl
Balanced domain
dc.subject.enpl
Lelong number
dc.subject.enpl
Bergman space
dc.subject.enpl
$L_{h}^{2}$-functions
dc.subject.enpl
$L_{h}^{2}$-domain of holomorphy
dc.subtypepl
Article
dc.titlepl
$L_{h}^{2}$-functions in unbounded balanced domains
dc.title.journalpl
The Journal of Geometric Analysis
dc.typepl
JournalArticle
dspace.entity.type
Publication

* The migration of download and view statistics prior to the date of April 8, 2024 is in progress.

Views
2
Views per month
Views per city
Ashburn
1
Downloads
L_{h}^{2}-functions in unbounded balanced domains.pdf
8

Open Access

Thumbnail Image
License
CC-BY

Except as otherwise noted, this item is licensed under : Udzielam licencji. Uznanie autorstwa 3.0 Polska

Collections
Research publications
Exact sciences