Commutant of multiplication operators in weighted Bergman spaces on polydisk

Ali Abkar

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 3, page 727-741
  • ISSN: 0011-4642

Abstract

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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 n -dimensional complex plane. Characterization of the commutant of such operators is given.

How to cite

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Abkar, Ali. "Commutant of multiplication operators in weighted Bergman spaces on polydisk." Czechoslovak Mathematical Journal 70.3 (2020): 727-741. <http://eudml.org/doc/297094>.

@article{Abkar2020,
abstract = {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 $n$-dimensional complex plane. Characterization of the commutant of such operators is given.},
author = {Abkar, Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {multiplication operator; commutant of an operator; weighted Bergman space},
language = {eng},
number = {3},
pages = {727-741},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Commutant of multiplication operators in weighted Bergman spaces on polydisk},
url = {http://eudml.org/doc/297094},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Abkar, Ali
TI - Commutant of multiplication operators in weighted Bergman spaces on polydisk
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 3
SP - 727
EP - 741
AB - 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 $n$-dimensional complex plane. Characterization of the commutant of such operators is given.
LA - eng
KW - multiplication operator; commutant of an operator; weighted Bergman space
UR - http://eudml.org/doc/297094
ER -

References

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  1. Abkar, A., 10.1006/jfan.2001.3851, J. Funct. Anal. 191 (2002), 224-240. (2002) Zbl1059.30049MR1911185DOI10.1006/jfan.2001.3851
  2. Abkar, A., 10.1090/S0002-9939-02-06491-2, Proc. Am. Math. Soc. 131 (2003), 155-164. (2003) Zbl1037.31002MR1929035DOI10.1090/S0002-9939-02-06491-2
  3. Abkar, A., On the commutant of certain operators in the Bergman space, Bull. Malays. Math. Sci. Soc. (2) 35 (2012), 499-502. (2012) Zbl1238.47023MR2912884
  4. Chattopadhyay, A., Das, A. B. Krishna, Sarkar, J., Sarkar, S., 10.1007/s00020-014-2128-y, Integral Equations Oper. Theory 79 (2014), 567-577. (2014) Zbl1328.47010MR3231245DOI10.1007/s00020-014-2128-y
  5. Chung, Y.-B., Na, H.-G., 10.5831/HMJ.2017.39.2.143, Honam Math. J. 39 (2017), 143-159. (2017) Zbl06798549MR3700286DOI10.5831/HMJ.2017.39.2.143
  6. Dan, H., Huang, H., 10.1007/s00020-014-2176-3, Integral Equations Oper. Theory 80 (2014), 581-601. (2014) Zbl1302.47061MR3279517DOI10.1007/s00020-014-2176-3
  7. Ding, X., Sang, Y., 10.1007/s00025-017-0728-y, Result. Math. 72 (2017), 1473-1497. (2017) Zbl06814121MR3721626DOI10.1007/s00025-017-0728-y
  8. Douglas, R. G., Banach Algebra Techniques in Operator Theory, Pure and Applied Mathematics 49, Academic Press, New York (1972). (1972) Zbl0247.47001MR0361893
  9. Duren, P., Schuster, A., 10.1090/surv/100, Mathematical Surveys and Monographs 100, American Mathematical Society, Providence (2004). (2004) Zbl1059.30001MR2033762DOI10.1090/surv/100
  10. Hedenmalm, H., Korenblum, B., Zhu, K., 10.1007/978-1-4612-0497-8, Graduate Texts in Mathematics 199, Springer, New York (2000). (2000) Zbl0955.32003MR1758653DOI10.1007/978-1-4612-0497-8
  11. Shi, Y., Lu, Y., 10.4134/BKMS.2013.50.2.687, Bull. Korean Math. Soc. 50 (2013), 687-696. (2013) Zbl1280.47039MR3137713DOI10.4134/BKMS.2013.50.2.687
  12. Zhu, K., 10.1112/S0024610700001198, J. Lond. Math. Soc., II. Ser. 62 (2000), 553-568. (2000) Zbl1158.47309MR1783644DOI10.1112/S0024610700001198
  13. Zhu, K., 10.1007/0-387-27539-8, Graduate Texts in Mathematics 226, Springer, New York (2005). (2005) Zbl1067.32005MR2115155DOI10.1007/0-387-27539-8

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