Open AccessSome results on the convergence of Hessian operator and $ m-$subharmonic functions
Author(s) -
Jawhar Hbil,
Mohamed Zaway
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022502
Subject(s) - hessian matrix , convergence (economics) , mathematics , subharmonic , converse , connection (principal bundle) , operator (biology) , sequence (biology) , measure (data warehouse) , mathematical analysis , pure mathematics , physics , nonlinear system , computer science , economics , geometry , chemistry , biochemistry , repressor , quantum mechanics , database , transcription factor , gene , economic growth
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.