Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 1139-1146, 2020

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

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

References:
[1] A. K. Al Abdulaali: The inductive wedge product of positive currents. J. Math. Anal. Appl. 412 (2014), 744-755. DOI 10.1016/j.jmaa.2013.10.072 | MR 3147245 | Zbl 1314.32049
[2] A. K. Al Abdulaali, H. El Mir: The existence problem of $S$-plurisubharmonic currents. C. R. Math., Acad. Sci. Paris 353 (2015), 605-610. DOI 10.1016/j.crma.2015.04.011 | MR 3352030 | Zbl 1321.32011
[3] E. Bishop: Conditions for the analyticity of certain sets. Mich. Math. J. 11 (1964), 289-304. DOI 10.1307/mmj/1028999180 | MR 0168801 | Zbl 0143.30302
[4] J.-P. Demailly: Monge-Ampère operators, Lelong numbers and intersection theory. Complex Analysis and Geometry University Series in Mathematics, Plenum Press, New York (1993), 115-193. DOI 10.1007/978-1-4757-9771-8_4 | MR 1211880 | Zbl 0792.32006
[5] J. E. Fornaess, N. Sibony: Oka's inequality for currents and applications. Math. Ann. 301 (1995), 399-419. DOI 10.1007/BF01446636 | MR 1324517 | Zbl 0832.32010
[6] B. Shiffman: On the removal of singularities of analytic sets. Mich. Math. J. 15 (1968), 111-120. DOI 10.1307/mmj/1028999912 | MR 0224865 | Zbl 0165.40503

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: aalabdulaaly@kfu.edu.sa, helmir@kfu.edu.sa

Springer subscribers can access the papers on Springer website.

[List of online first articles] [Contents of Czechoslovak Mathematical Journal] [Full text of the older issues of Czechoslovak Mathematical Journal at DML-CZ]

PDF available at:

Springer
for subscribers

···

Institute of Mathematics CAS
free access

···

Digital Mathematics Library
free access