Complex analysis/Functional analysis
Weighted-composition operators on Np-spaces in the ball
Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 719-723.

In this Note, we introduce Np-spaces, some kind of Bergman-type spaces, of holomorphic functions in the unit ball of Cn. Basic properties of these spaces are provided. We study weighted-composition operators between Np-spaces and the spaces Aq and obtain, in particular, criteria for boundedness and compactness of such operators.

Dans cette Note, nous introduisons les espaces Np, qui sont des analogues dʼespaces de Bergman de fonctions holomorphes sur la boule unité de Cn. Les propriétés de base de ces espaces sont données. Nous étudions ensuite les opérateurs de composition à poids de Np dans Aq, et nous obtenons, en particulier, des critères pour que ces opérateurs soient bornés ou compacts.

Published online:
DOI: 10.1016/j.crma.2013.10.002
Hu, Bingyang 1; Khoi, Le Hai 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
     author = {Hu, Bingyang and Khoi, Le Hai},
     title = {Weighted-composition operators on $ {\mathcal{N}}_{p}$-spaces in the ball},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {719--723},
     publisher = {Elsevier},
     volume = {351},
     number = {19-20},
     year = {2013},
     doi = {10.1016/j.crma.2013.10.002},
     language = {en},
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Hu, Bingyang; Khoi, Le Hai. Weighted-composition operators on $ {\mathcal{N}}_{p}$-spaces in the ball. Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 719-723. doi : 10.1016/j.crma.2013.10.002.

[1] Cowen, C.; MacCluer, B. Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995

[2] Hedenmalm, H.; Korenblum, B.; Zhu, K. Theory of Bergman Spaces, Springer-Verlag, 2000

[3] Krantz, S. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992

[4] Palmberg, N. Composition operator acting on Np-spaces, Bull. Belg. Math. Soc., Volume 14 (2007), pp. 545-554

[5] Rudin, W. Function Theory in the Unit Ball of Cn, Springer-Verlag, New York, 1980

[6] Shapiro, J.H. Compositions Operators and Classical Function Theory, Springer-Verlag, New York, 1993

[7] Ueki, S. Weighted composition operators acting between the Np-space and the weighted-type space Hα, Indag. Math., Volume 23 (2012), pp. 243-255

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