| Title:
|
Controlling products of currents by higher powers of plurisubharmonic functions (English) |
| Author:
|
Al Abdulaali, Ahmad K. |
| Author:
|
El Mir, Hassine |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
1139-1146 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
positive current |
| Keyword:
|
plurisubharmonic function |
| Keyword:
|
plurisubharmonic current |
| MSC:
|
32U40 |
| idZBL:
|
07285985 |
| idMR:
|
MR4181802 |
| DOI:
|
10.21136/CMJ.2020.0205-19 |
| . |
| Date available:
|
2020-11-18T09:48:57Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148417 |
| . |
| Reference:
|
[1] Abdulaali, A. K. Al: The inductive wedge product of positive currents.J. Math. Anal. Appl. 412 (2014), 744-755. Zbl 1314.32049, MR 3147245, 10.1016/j.jmaa.2013.10.072 |
| Reference:
|
[2] Abdulaali, A. K. Al, Mir, H. El: The existence problem of $S$-plurisubharmonic currents.C. R. Math., Acad. Sci. Paris 353 (2015), 605-610. Zbl 1321.32011, MR 3352030, 10.1016/j.crma.2015.04.011 |
| Reference:
|
[3] Bishop, E.: Conditions for the analyticity of certain sets.Mich. Math. J. 11 (1964), 289-304. Zbl 0143.30302, MR 0168801, 10.1307/mmj/1028999180 |
| Reference:
|
[4] Demailly, J.-P.: Monge-Ampère operators, Lelong numbers and intersection theory.Complex Analysis and Geometry University Series in Mathematics, Plenum Press, New York (1993), 115-193. Zbl 0792.32006, MR 1211880, 10.1007/978-1-4757-9771-8_4 |
| Reference:
|
[5] ss, J. E. Fornæ, Sibony, N.: Oka's inequality for currents and applications.Math. Ann. 301 (1995), 399-419. Zbl 0832.32010, MR 1324517, 10.1007/BF01446636 |
| Reference:
|
[6] Shiffman, B.: On the removal of singularities of analytic sets.Mich. Math. J. 15 (1968), 111-120. Zbl 0165.40503, MR 0224865, 10.1307/mmj/1028999912 |
| . |
