Capacity and stability on some Cegrell classes of m− subharmonic functions

• Hbil, Jawhar ^[1] ; Zaway, Mohamed ^[2]
  1. [1] Department of Mathematics Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia
  2. [2] Department of mathematics, College of science, Shaqra University, P.O. box 1040, Ad-Dwadimi, 1191, Kingdom of Saudi Arabia
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 3, 2023, págs. 817-835
• Idioma: inglés
• DOI: 10.1007/s13348-022-00374-5
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• Resumen

  • The aim of this paper is to show some equivalent conditions to the convergence in m−capacity for a sequence of m−subharmonic functions based on its Hessian measure. As an application, we prove a stability theorem which is analogous to Cegrell and Kołodziej theorem from [14].