Complex Hessian-type equations in the weighted $m$-subharmonic class
UDC 517.5 We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure $\mu$ defined on an $m$-hyperconvex domain  $\Omega \subset \mathbb{C}^n,$  under  suitable condi...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7122 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512605862363136 |
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| author | Zaway, Mohamed Hbil, Jawhar Zaway, Mohamed Hbil, Jawhar |
| author_facet | Zaway, Mohamed Hbil, Jawhar Zaway, Mohamed Hbil, Jawhar |
| author_sort | Zaway, Mohamed |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-07-02T07:08:15Z |
| description | UDC 517.5
We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure $\mu$ defined on an $m$-hyperconvex domain  $\Omega \subset \mathbb{C}^n,$  under  suitable conditions, we prove that the equation $\chi(.) H_m(.)=\mu$ has a solution that belongs to the class $\mathcal{E}_{m,\chi}(\Omega).$ |
| doi_str_mv | 10.37863/umzh.v75i6.7122 |
| first_indexed | 2026-03-24T03:31:27Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7122 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:27Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-71222023-07-02T07:08:15Z Complex Hessian-type equations in the weighted $m$-subharmonic class Complex Hessian-type equations in the weighted $m$-subharmonic class Zaway, Mohamed Hbil, Jawhar Zaway, Mohamed Hbil, Jawhar m-subharmonic function Capacity Hessian operator. UDC 517.5 We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure $\mu$ defined on an $m$-hyperconvex domain  $\Omega \subset \mathbb{C}^n,$  under  suitable conditions, we prove that the equation $\chi(.) H_m(.)=\mu$ has a solution that belongs to the class $\mathcal{E}_{m,\chi}(\Omega).$ УДК 517.5 Комплексні рівняння типу Гессе у зваженому $m$-субгармонічному класі Досліджено існування розв’язку для комплексного рівняння Гессе загального типу на деяких класах Сегрелля. Для заданої міри $\mu$, що визначена на $m$-гіперопуклій області $\Omega \subset \mathbb{C}^n,$  доведено, що за відповідних умов  рівняння $\chi(.) H_m(.)= \mu$ має розв’язок, який належить класу $\mathcal{E}_{m,\chi}(\Omega).$ Institute of Mathematics, NAS of Ukraine 2023-06-20 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7122 10.37863/umzh.v75i6.7122 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 6 (2023); 805 - 816 Український математичний журнал; Том 75 № 6 (2023); 805 - 816 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7122/9764 Copyright (c) 2023 mohamed zaway |
| spellingShingle | Zaway, Mohamed Hbil, Jawhar Zaway, Mohamed Hbil, Jawhar Complex Hessian-type equations in the weighted $m$-subharmonic class |
| title | Complex Hessian-type equations in the weighted $m$-subharmonic class |
| title_alt | Complex Hessian-type equations in the weighted $m$-subharmonic class |
| title_full | Complex Hessian-type equations in the weighted $m$-subharmonic class |
| title_fullStr | Complex Hessian-type equations in the weighted $m$-subharmonic class |
| title_full_unstemmed | Complex Hessian-type equations in the weighted $m$-subharmonic class |
| title_short | Complex Hessian-type equations in the weighted $m$-subharmonic class |
| title_sort | complex hessian-type equations in the weighted $m$-subharmonic class |
| topic_facet | m-subharmonic function Capacity Hessian operator. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7122 |
| work_keys_str_mv | AT zawaymohamed complexhessiantypeequationsintheweightedmsubharmonicclass AT hbiljawhar complexhessiantypeequationsintheweightedmsubharmonicclass AT zawaymohamed complexhessiantypeequationsintheweightedmsubharmonicclass AT hbiljawhar complexhessiantypeequationsintheweightedmsubharmonicclass |