Some results on the convergence of Hessian operator and m−subharmonic functions
In this paper we treat the problem of connection between the convergence in $ m- $capacity and the convergence of the Hessian measure for a sequence$ f_j $ of $ m- $subharmonic functions. We prove first that, under some conditions, the convergence of $ f_j $ in capacity $ Cap_m $ implies the weak co...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022502?viewType=HTML |
| _version_ | 1818271032284282880 |
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| author | Jawhar Hbil Mohamed Zaway |
| author_facet | Jawhar Hbil Mohamed Zaway |
| author_sort | Jawhar Hbil |
| collection | DOAJ |
| description | In this paper we treat the problem of connection between the convergence in $ m- $capacity and the convergence of the Hessian measure for a sequence$ f_j $ of $ m- $subharmonic functions. We prove first that, under some conditions, the convergence of $ f_j $ in capacity $ Cap_m $ implies the weak convergence of the Hessian measures $ H_m(f_j) $. Then we show that the converse sense of convergence is also true in some particular cases. |
| first_indexed | 2024-12-12T21:19:43Z |
| format | Article |
| id | doaj.art-0d70cb954be94d30ada0c45cdaa12fa7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T21:19:43Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-0d70cb954be94d30ada0c45cdaa12fa72022-12-22T00:11:38ZengAIMS PressAIMS Mathematics2473-69882022-03-01759023903810.3934/math.2022502Some results on the convergence of Hessian operator and m−subharmonic functionsJawhar Hbil 0Mohamed Zaway11. Department of Mathematics, College of science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia2. Department of mathematics, College of science, Shaqra University, P.O. Box 1040, Ad-Dwadimi 1191, Saudi ArabiaIn this paper we treat the problem of connection between the convergence in $ m- $capacity and the convergence of the Hessian measure for a sequence$ f_j $ of $ m- $subharmonic functions. We prove first that, under some conditions, the convergence of $ f_j $ in capacity $ Cap_m $ implies the weak convergence of the Hessian measures $ H_m(f_j) $. Then we show that the converse sense of convergence is also true in some particular cases.https://www.aimspress.com/article/doi/10.3934/math.2022502?viewType=HTMLm−subharmonic functionm−capacityhessian operator |
| spellingShingle | Jawhar Hbil Mohamed Zaway Some results on the convergence of Hessian operator and m−subharmonic functions AIMS Mathematics m−subharmonic function m−capacity hessian operator |
| title | Some results on the convergence of Hessian operator and m−subharmonic functions |
| title_full | Some results on the convergence of Hessian operator and m−subharmonic functions |
| title_fullStr | Some results on the convergence of Hessian operator and m−subharmonic functions |
| title_full_unstemmed | Some results on the convergence of Hessian operator and m−subharmonic functions |
| title_short | Some results on the convergence of Hessian operator and m−subharmonic functions |
| title_sort | some results on the convergence of hessian operator and m subharmonic functions |
| topic | m−subharmonic function m−capacity hessian operator |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022502?viewType=HTML |
| work_keys_str_mv | AT jawharhbil someresultsontheconvergenceofhessianoperatorandmsubharmonicfunctions AT mohamedzaway someresultsontheconvergenceofhessianoperatorandmsubharmonicfunctions |