Controlling products of currents by higher powers of plurisubharmonic functions

Ahmad K. Al Abdulaali; Hassine El Mir

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 4, page 1139-1146
  • ISSN: 0011-4642

Abstract

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We discuss the existence of the current g k T , k ∈ 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.

How to cite

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Al Abdulaali, Ahmad K., and El Mir, Hassine. "Controlling products of currents by higher powers of plurisubharmonic functions." Czechoslovak Mathematical Journal 70.4 (2020): 1139-1146. <http://eudml.org/doc/296936>.

@article{AlAbdulaali2020,
abstract = {We discuss the existence of the current $g^\{k\}T$, $k \in \mathbb \{N\}$ 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.},
author = {Al Abdulaali, Ahmad K., El Mir, Hassine},
journal = {Czechoslovak Mathematical Journal},
keywords = {positive current; plurisubharmonic function; plurisubharmonic current},
language = {eng},
number = {4},
pages = {1139-1146},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Controlling products of currents by higher powers of plurisubharmonic functions},
url = {http://eudml.org/doc/296936},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Al Abdulaali, Ahmad K.
AU - El Mir, Hassine
TI - Controlling products of currents by higher powers of plurisubharmonic functions
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 1139
EP - 1146
AB - We discuss the existence of the current $g^{k}T$, $k \in \mathbb {N}$ 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.
LA - eng
KW - positive current; plurisubharmonic function; plurisubharmonic current
UR - http://eudml.org/doc/296936
ER -

References

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  1. Abdulaali, A. K. Al, 10.1016/j.jmaa.2013.10.072, J. Math. Anal. Appl. 412 (2014), 744-755. (2014) Zbl1314.32049MR3147245DOI10.1016/j.jmaa.2013.10.072
  2. Abdulaali, A. K. Al, Mir, H. El, 10.1016/j.crma.2015.04.011, C. R. Math., Acad. Sci. Paris 353 (2015), 605-610. (2015) Zbl1321.32011MR3352030DOI10.1016/j.crma.2015.04.011
  3. Bishop, E., 10.1307/mmj/1028999180, Mich. Math. J. 11 (1964), 289-304. (1964) Zbl0143.30302MR0168801DOI10.1307/mmj/1028999180
  4. Demailly, J.-P., 10.1007/978-1-4757-9771-8_4, Complex Analysis and Geometry University Series in Mathematics, Plenum Press, New York (1993), 115-193. (1993) Zbl0792.32006MR1211880DOI10.1007/978-1-4757-9771-8_4
  5. ss, J. E. Fornæ, Sibony, N., 10.1007/BF01446636, Math. Ann. 301 (1995), 399-419. (1995) Zbl0832.32010MR1324517DOI10.1007/BF01446636
  6. Shiffman, B., 10.1307/mmj/1028999912, Mich. Math. J. 15 (1968), 111-120. (1968) Zbl0165.40503MR0224865DOI10.1307/mmj/1028999912

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