Weighted-composition operators on $ {\mathcal{N}}_{p}$-spaces in the ball

Bingyang Hu; Le Hai Khoi

doi:10.1016/j.crma.2013.10.002

Complex analysis/Functional analysis

Weighted-composition operators on

N_{p}

-spaces in the ball

Présenté par : Jean-Pierre Demailly

Bingyang Hu ¹ ; Le Hai Khoi ¹

¹ Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore

Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 719-723.

Résumé
Abstract

Dans cette Note, nous introduisons les espaces $N_{p}$ , qui sont des analogues dʼespaces de Bergman de fonctions holomorphes sur la boule unité de $C^{n}$ . Les propriétés de base de ces espaces sont données. Nous étudions ensuite les opérateurs de composition à poids de $N_{p}$ dans $A^{- q}$ , et nous obtenons, en particulier, des critères pour que ces opérateurs soient bornés ou compacts.

In this Note, we introduce $N_{p}$ -spaces, some kind of Bergman-type spaces, of holomorphic functions in the unit ball of $C^{n}$ . Basic properties of these spaces are provided. We study weighted-composition operators between $N_{p}$ -spaces and the spaces $A^{- q}$ and obtain, in particular, criteria for boundedness and compactness of such operators.

Reçu le : 2013-05-21
Accepté le : 2013-10-03
Publié le : 2013-10-01

DOI : 10.1016/j.crma.2013.10.002

Affiliations des auteurs :

Bingyang Hu ¹ ; Le Hai Khoi ¹

¹ Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore

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     author = {Bingyang Hu and Le Hai Khoi},
     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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Bingyang Hu; Le Hai Khoi. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.002/

Bibliographie
Cité par

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

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

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

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

[5] W. Rudin Function Theory in the Unit Ball of $C^{n}$ , Springer-Verlag, New York, 1980

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

[7] S. Ueki Weighted composition operators acting between the $N_{p}$ -space and the weighted-type space $H_{α}^{\infty}$ , Indag. Math., Volume 23 (2012), pp. 243-255

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