| Title:
|
Commutant of multiplication operators in weighted Bergman spaces on polydisk (English) |
| Author:
|
Abkar, Ali |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
727-741 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the \hbox {$n$-dimensional} complex plane. Characterization of the commutant of such operators is given. (English) |
| Keyword:
|
multiplication operator |
| Keyword:
|
commutant of an operator |
| Keyword:
|
weighted Bergman space |
| MSC:
|
30H20 |
| MSC:
|
32A36 |
| MSC:
|
46E22 |
| MSC:
|
47B38 |
| idZBL:
|
07250685 |
| idMR:
|
MR4151701 |
| DOI:
|
10.21136/CMJ.2020.0494-18 |
| . |
| Date available:
|
2020-09-07T09:36:48Z |
| Last updated:
|
2022-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148324 |
| . |
| Reference:
|
[1] Abkar, A.: Norm approximation by polynomials in some weighted Bergman spaces.J. Funct. Anal. 191 (2002), 224-240. Zbl 1059.30049, MR 1911185, 10.1006/jfan.2001.3851 |
| Reference:
|
[2] Abkar, A.: Application of a Riesz-type formula to weighted Bergman spaces.Proc. Am. Math. Soc. 131 (2003), 155-164. Zbl 1037.31002, MR 1929035, 10.1090/S0002-9939-02-06491-2 |
| Reference:
|
[3] Abkar, A.: On the commutant of certain operators in the Bergman space.Bull. Malays. Math. Sci. Soc. (2) 35 (2012), 499-502. Zbl 1238.47023, MR 2912884 |
| Reference:
|
[4] Chattopadhyay, A., Das, A. B. Krishna, Sarkar, J., Sarkar, S.: Wandering subspaces of the Bergman space and the Dirichlet space over $\mathbb{D}^n$.Integral Equations Oper. Theory 79 (2014), 567-577. Zbl 1328.47010, MR 3231245, 10.1007/s00020-014-2128-y |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[9] Duren, P., Schuster, A.: Bergman Spaces.Mathematical Surveys and Monographs 100, American Mathematical Society, Providence (2004). Zbl 1059.30001, MR 2033762, 10.1090/surv/100 |
| Reference:
|
[10] Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces.Graduate Texts in Mathematics 199, Springer, New York (2000). Zbl 0955.32003, MR 1758653, 10.1007/978-1-4612-0497-8 |
| Reference:
|
[11] Shi, Y., Lu, Y.: Reducing subspaces for Toeplitz operators on the polydisk.Bull. Korean Math. Soc. 50 (2013), 687-696. Zbl 1280.47039, MR 3137713, 10.4134/BKMS.2013.50.2.687 |
| Reference:
|
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| Reference:
|
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| . |
