Weighted sub-Bergman Hilbert spaces
Maria Nowak ; Renata Rososzczuk
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 68 (2014), / Harvested from The Polish Digital Mathematics Library

We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces Aα2, 1<α<. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:289730
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     author = {Maria Nowak and Renata Rososzczuk},
     title = {Weighted sub-Bergman Hilbert spaces},
     journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
     volume = {68},
     year = {2014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_49}
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Maria Nowak; Renata Rososzczuk. Weighted sub-Bergman Hilbert spaces. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 68 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_49/

Abkar, A., Jafarzadeh, B., Weighted sub-Bergman Hilbert spaces in the unit disk, Czechoslovak Math. J. 60 (2010), 435-443.

Cowen, C., MacCluer, B., Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.

Hedenmalm, H., Korenblum, B., Zhu, K., Theory of Bergman Spaces, Spinger-Verlag, New York, 2000.

Sarason, D., Sub-Hardy Hilbert Spaces in the Unit Disk, Wiley, New York, 1994.

Sultanic, S., Sub-Bergman Hilbert spaces, J. Math. Anal. Appl. 324 (2006), 639-649.

Symesak, F., Sub-Bergman spaces in the unit ball of Cn, Proc. Amer. Math. Soc. 138 (2010), 4405-4411.

Zhu, K., Sub-Bergman Hilbert spaces in the unit disk, Indiana Univ. Math. J. 45 (1996), 165-176.

Zhu, K., Sub-Bergman Hilbert spaces in the unit disk, II, J. Funct. Anal. 202 (2003), 327-341.

Zhu, K., Operator Theory in Function Spaces, Dekker, New York, 1990.

Zorboska, N., Composition operators induced by functons with supremum strictly smaller than 1, Proc. Amer. Math. Soc. 106 (1989), 679-684.