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Research Article | Open Access

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

Jawhar Hbil1( ), Mohamed Zaway2
Department of Mathematics, College of science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia
Department of mathematics, College of science, Shaqra University, P.O. Box 1040, Ad-Dwadimi 1191, Saudi Arabia
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Abstract

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 C a p 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.

Keywords

m−subharmonic functionm−CapacityHessian operator
CLC number: 32U40, 32U05, 32U20

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9023-9038
DOI: 10.3934/math.2022502

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Cite this article:
Hbil J, Zaway M. Some results on the convergence of Hessian operator and m −subharmonic functions. AIMS Mathematics, 2022, 7(5): 9023-9038. https://doi.org/10.3934/math.2022502

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Received: 19 October 2021
Revised: 17 February 2022
Accepted: 28 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)