Geodesic
Weighted sub-Bergman Hilbert spaces
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 68 (2014) no. 1 
Nowak, Maria; Rososzczuk, Renata. Weighted sub-Bergman Hilbert spaces. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 68 (2014) no. 1. http://geodesic.mathdoc.fr/item/AUM_2014_68_1_a7/
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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^2_α, −1 lt; α lt; ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.

[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.