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Filomat 2024 Volume 38, Issue 5, Pages: 1613-1622
https://doi.org/10.2298/FIL2405613H
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Convergence for m−positive currents and m−subharmonic functions

Hbil Jawhar (Department of Mathematics, Jouf University, Sakaka, Saudi Arabia), jmhbil@ju.edu.sa
Zaway Mohamed (Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, Sfax, Tunisia + Irescomath Laboratory, Gabes University, Zrig Gabes, Tunisia), mohamed_zaway@yahoo.fr

In this paper we give sufficient conditions on m−subharmonic functions fk and m−positive currents Rk of bidegree (p,p) to ensure the convergence of fk.Rk∧γm−p in the sense of currents. As application of this result, we treat the special case Rk=(ddcfk)p and we show that one of the condition of the main result is necessary in this case.

Keywords: Monge-Ampère operator, m−subharmonic function, Capacity, m−positive closed current


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