Czechoslovak Mathematical Journal, first online, pp. 1-8

Controlling products of currents by higher powers of plurisubharmonic functions

Ahmad K. Al Abdulaali, Hassine El Mir

Received May 7, 2019.   Published online July 7, 2020.

Abstract:  We discuss the existence of the current $g^kT$, $k \in\mathbb N$ for positive and closed currents $T$ and unbounded plurisubharmonic functions $g$. Furthermore, a new type of weighted Lelong number is introduced under the name of weight $k$ Lelong number.
Keywords:  positive current; plurisubharmonic function; plurisubharmonic current
Classification MSC:  32U40
DOI:  10.21136/CMJ.2020.0205-19

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Affiliations:   Ahmad K. Al Abdulaali (corresponding author), Hassine El Mir, The Department of Mathematics, College of Science, King Faisal University, P.O. Box 380, 31982 Al-Ahsaa, Saudi Arabia, e-mail:,

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