Weighted sub-Bergman Hilbert spaces

Maria Nowak; Renata Rososzczuk

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2014)

  • Volume: 68, Issue: 1
  • ISSN: 0365-1029

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 A α 2 , − 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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 68.1 (2014): null. <http://eudml.org/doc/289730>.

@article{MariaNowak2014,
abstract = {We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces $A^2_\{\alpha \}$, $−1 < \alpha < \infty $. 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 Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {},
language = {eng},
number = {1},
pages = {null},
title = {Weighted sub-Bergman Hilbert spaces},
url = {http://eudml.org/doc/289730},
volume = {68},
year = {2014},
}

TY - JOUR
AU - Maria Nowak
AU - Renata Rososzczuk
TI - Weighted sub-Bergman Hilbert spaces
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2014
VL - 68
IS - 1
SP - null
AB - We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces $A^2_{\alpha }$, $−1 < \alpha < \infty $. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.
LA - eng
KW -
UR - http://eudml.org/doc/289730
ER -

References

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

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