Weighted sub-Bergman Hilbert spaces

Maria Nowak; Renata Rososzczuk

Annales UMCS, Mathematica (2014)

  • Volume: 68, Issue: 1, page 49-57
  • ISSN: 2083-7402

Abstract

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We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A2α, −1 < α < ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers

How to cite

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Maria Nowak, and Renata Rososzczuk. "Weighted sub-Bergman Hilbert spaces." Annales UMCS, Mathematica 68.1 (2014): 49-57. <http://eudml.org/doc/267336>.

@article{MariaNowak2014,
abstract = {We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A2α, −1 < α < ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers},
author = {Maria Nowak, Renata Rososzczuk},
journal = {Annales UMCS, Mathematica},
keywords = {Weighted Bergman spaces; Toeplitz operators; weighted Bergman spaces},
language = {eng},
number = {1},
pages = {49-57},
title = {Weighted sub-Bergman Hilbert spaces},
url = {http://eudml.org/doc/267336},
volume = {68},
year = {2014},
}

TY - JOUR
AU - Maria Nowak
AU - Renata Rososzczuk
TI - Weighted sub-Bergman Hilbert spaces
JO - Annales UMCS, Mathematica
PY - 2014
VL - 68
IS - 1
SP - 49
EP - 57
AB - We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A2α, −1 < α < ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers
LA - eng
KW - Weighted Bergman spaces; Toeplitz operators; weighted Bergman spaces
UR - http://eudml.org/doc/267336
ER -

References

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  1. [1] Abkar, A., Jafarzadeh, B., Weighted sub-Bergman Hilbert spaces in the unit disk, Czechoslovak Math. J. 60 (2010), 435-443. Zbl1220.47033
  2. [2] Cowen, C., MacCluer, B., Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995. Zbl0873.47017
  3. [3] Hedenmalm, H., Korenblum, B., Zhu, K., Theory of Bergman Spaces, Spinger-Verlag, New York, 2000. Zbl0955.32003
  4. [4] Sarason, D., Sub-Hardy Hilbert Spaces in the Unit Disk, Wiley, New York, 1994. Zbl1253.30002
  5. [5] Sultanic, S., Sub-Bergman Hilbert spaces, J. Math. Anal. Appl. 324 (2006), 639-649. Zbl1115.46021
  6. [6] Symesak, F., Sub-Bergman spaces in the unit ball of Cn, Proc. Amer. Math. Soc. 138 (2010), 4405-4411.[WoS] Zbl1208.32006
  7. [7] Zhu, K., Sub-Bergman Hilbert spaces in the unit disk, Indiana Univ. Math. J. 45 (1996), 165-176. Zbl0863.30051
  8. [8] Zhu, K., Sub-Bergman Hilbert spaces in the unit disk, II, J. Funct. Anal. 202 (2003), 327-341. Zbl1039.47019
  9. [9] Zhu, K., Operator Theory in Function Spaces, Dekker, New York, 1990. Zbl0706.47019
  10. [10] Zorboska, N., Composition operators induced by functons with supremum strictly smaller than 1, Proc. Amer. Math. Soc. 106 (1989), 679-684. Zbl0686.47027

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