Comptes Rendus
no. 1-2
Mathematical Analysis
On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces
[Sur un critère de continuité et compacité des opérateurs de composition agissant sur les espaces α-Bloch]

Présenté par : Jean-Pierre Kahane

María T. Malavé Ramírez1 ; Julio C. Ramos Fernández1
1 Departamento de Matemática, Universidad de Oriente, 6101 Cumaná, Edo. Sucre, Venezuela
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 23-26.

Dans cette Note, nous donnons un nouveau critère pour la continuité et la compacité des opérateurs de composition agissant sur les espaces α-Bloch.

In this Note we give a new criterion for the continuity and compactness of composition operators acting on α-Bloch spaces.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.11.013
María T. Malavé Ramírez 1 ; Julio C. Ramos Fernández 1

1 Departamento de Matemática, Universidad de Oriente, 6101 Cumaná, Edo. Sucre, Venezuela 
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María T. Malavé Ramírez; Julio C. Ramos Fernández. On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 23-26. doi : 10.1016/j.crma.2012.11.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.11.013/

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[2] K. Madigan; A. Matheson Compact composition operators on the Bloch space, Trans. Amer. Math. Soc., Volume 347 (1995), pp. 2679-2687

[3] J.C. Ramos-Fernández Composition operators between μ-Bloch spaces, Extracta Math., Volume 26 (2011) no. 1, pp. 75-88

[4] M. Tjani, Compact composition operators on some Möbius invariant Banach space, PhD dissertation, Michigan State University, 1996.

[5] M. Tjani Compact composition operators on Besov spaces, Trans. Amer. Math. Soc., Volume 355 (2003) no. 11, pp. 4683-4698

[6] H. Wulan Compactness of composition operators on BMOA and VMOA, Sci. China Ser. A, Volume 50 (2007) no. 7, pp. 997-1004

[7] H. Wulan; D. Zheng; K. Zhu Compact composition operators on BMO and the Bloch space, Proc. Amer. Math. Soc., Volume 137 (2009), pp. 3861-3868

[8] J. Xiao Composition operators associated with Bloch-type spaces, Complex Var. Theory Appl., Volume 46 (2001), pp. 109-121

[9] R. Zhao Essential norms of composition operators between Bloch type spaces, Proc. Amer. Math. Soc., Volume 138 (2010), pp. 2537-2546

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