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Some results on the convergence of Hessian operator and m-subharmonic functions
Journal article   Open access  Peer reviewed

Some results on the convergence of Hessian operator and m-subharmonic functions

Jawhar Hbil, Mohamed Zaway and Department of Mathematics, College of science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia
AIMS mathematics, Vol.7(5), pp.9023-9038
01/01/2022
DOI: https://doi.org/10.3934/math.2022502

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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.
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https://doi.org/10.3934/math.2022502View
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