Weighted sub-Bergman Hilbert spaces in the unit disk

Ali Abkar; B. Jafarzadeh

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 435-443
  • ISSN: 0011-4642

Abstract

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We study sub-Bergman Hilbert spaces in the weighted Bergman space . We generalize the results already obtained by Kehe Zhu for the standard Bergman space .

How to cite

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Abkar, Ali, and Jafarzadeh, B.. "Weighted sub-Bergman Hilbert spaces in the unit disk." Czechoslovak Mathematical Journal 60.2 (2010): 435-443. <http://eudml.org/doc/38018>.

@article{Abkar2010,
abstract = {We study sub-Bergman Hilbert spaces in the weighted Bergman space $A^2_\alpha $. We generalize the results already obtained by Kehe Zhu for the standard Bergman space $A^2$.},
author = {Abkar, Ali, Jafarzadeh, B.},
journal = {Czechoslovak Mathematical Journal},
keywords = {weighted Bergman space; sub-Bergman Hilbert space; weighted Toeplitz operator; reproducing kernel; weighted Bergman space; sub-Bergman Hilbert space; weighted Toeplitz operator; reproducing kernel},
language = {eng},
number = {2},
pages = {435-443},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weighted sub-Bergman Hilbert spaces in the unit disk},
url = {http://eudml.org/doc/38018},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Abkar, Ali
AU - Jafarzadeh, B.
TI - Weighted sub-Bergman Hilbert spaces in the unit disk
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 435
EP - 443
AB - We study sub-Bergman Hilbert spaces in the weighted Bergman space $A^2_\alpha $. We generalize the results already obtained by Kehe Zhu for the standard Bergman space $A^2$.
LA - eng
KW - weighted Bergman space; sub-Bergman Hilbert space; weighted Toeplitz operator; reproducing kernel; weighted Bergman space; sub-Bergman Hilbert space; weighted Toeplitz operator; reproducing kernel
UR - http://eudml.org/doc/38018
ER -

References

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  1. Hedenmalm, H., Korenblum, B., Zhu, K., 10.1007/978-1-4612-0497-8_1, Graduate Texts in Mathematics, Vol. 199, Springer-Verlag, New York (2000). (2000) Zbl0955.32003MR1758653DOI10.1007/978-1-4612-0497-8_1
  2. Sarason, D., Sub-Hardy Hilbert Spaces in the Unit Disk, John Wiley and Sons Inc., New York (1994). (1994) MR1289670
  3. Saitoh, S., Thoery of Reproducing Kernels and its Applications, Pitman Research Notes in Mathematics, Vol. 189, New York (1988). (1988) MR0983117
  4. Sultanic, S., 10.1016/j.jmaa.2005.12.035, J. Math. Anal. Appl. 324 (2006), 639-649. (2006) Zbl1115.46021MR2262497DOI10.1016/j.jmaa.2005.12.035
  5. Zhu, K., Sub-Bergman Hilbert spaces in the unit disk, Indiana Univ. Math. J. 45 (1996), 165-176. (1996) MR1406688
  6. Zhu, K., 10.1016/S0022-1236(02)00086-1, J. Func. Anal. 202 (2003), 327-341. (2003) Zbl1039.47019MR1990528DOI10.1016/S0022-1236(02)00086-1
  7. Zhu, K., Operator Theory in Function Spaces, Dekker, New York (1990). (1990) Zbl0706.47019MR1074007

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