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
Main Authors: Zaway, Mohamed, Hbil, Jawhar
Format: Article
Language:English
Published: Institute of Mathematics, NAS of Ukraine 2023
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
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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 $\mathcal{E}_{m,\chi}(\Omega).$
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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
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AT hbiljawhar complexhessiantypeequationsintheweightedmsubharmonicclass
AT zawaymohamed complexhessiantypeequationsintheweightedmsubharmonicclass
AT hbiljawhar complexhessiantypeequationsintheweightedmsubharmonicclass