A note on the space of delta <em>m</em>-subharmonic functions

Van Thien Nguyen; Samsul Ariffin Abdul Karim; Dinh Dat Truong; Van Thien Nguyen; Samsul Ariffin Abdul Karim; Dinh Dat Truong

doi:10.3934/math.2020156

AIMS Mathematics

2020, Volume 5, Issue 3: 2369-2375. doi: 10.3934/math.2020156

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Research article

A note on the space of delta m-subharmonic functions

1.
FPT University, Education zone, Hoa Lac high tech park, Km29 Thang Long highway, Thach That ward, Hanoi, Vietnam
2.
Fundamental and Applied Sciences Department and Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia
3.
Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay District, Hanoi, Vietnam

Received: 29 October 2019 Accepted: 25 February 2020 Published: 04 March 2020
MSC : 32U15, 32U20

In this note, we present some properties of a certain space of delta m-subharmonic functions. We prove that the convergence in this space implies the convergence in m-capacity.
- m-subharmonic functions,
- complex Hessian equations,
- quasi-Banach space,
- convergence in capacity
Citation: Van Thien Nguyen, Samsul Ariffin Abdul Karim, Dinh Dat Truong. A note on the space of delta m-subharmonic functions[J]. AIMS Mathematics, 2020, 5(3): 2369-2375. doi: 10.3934/math.2020156

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Abstract

In this note, we present some properties of a certain space of delta m-subharmonic functions. We prove that the convergence in this space implies the convergence in m-capacity.

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