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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.15 no.3 Temuco  2013 


Composition operators in hyperbolic general Besov-type spaces


A. El-Sayed Ahmed1,2 and M. A. Bakhit3

1Sohag University, Faculty of Science, Department of Mathematics, 82524 Sohag, Egypt.

2Taif University, Faculty of Science, Mathematics, Department, box 888 El-Hawiyah, El-Taif 5700, Saudi Arabia.

3Department of Mathematics, Faculty of Science, Assiut Branch, Al-Azhar University, Assiut 32861, Egypt.


In this paper we introduce natural metrics in the hyperbolic α-Bloch and hyperbolic general Besov-type classes F*(p, q, s). These classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, compact composition operators acting from the hyperbolic α-Bloch class to the class F*(p, q, s) are characterized by conditions depending on an analytic self-map : D D.

Keywords and Phrases: Hyperbolic classes, composition operators, Lipschitz continuous, α-Bloch space, F*(p, q, s) class.


En este artículo introducimos una métrica natural en las clases hiperbólicas α-Bloch y tipo Besov generales. Estas clases se muestra que son espacios métricos completos respecto de las métricas correspondientes. Además se caracterizan los operadores de composición compactos que actúan desde las clases hiperbólicas α-Bloch en la clase F*(p, q, s) por condiciones que dependen de la autoaplicación analítica : D D.

2010 AMS Mathematics Subject Classification: 47B38, 30D50, 30D45, 46E15.



[1] A. El-Sayed Ahmed, Natural metrics and composition operators in generalized hyperbolic function spaces, Journal of inequalities and applications, 185(2012), 1-12.         [ Links ]

[2] A. El-Sayed Ahmed and M. A. Bakhit, Composition operators on some holomorphic Banach function spaces, Mathematica Scandinavica, 104(2)(2009), 275-295.         [ Links ]

[3] A. El-Sayed Ahmed and M. A. Bakhit, Composition operators acting between some weighted Möbius invariant spaces, Ann. Funct. Anal. AFA 2(2)(2011), 138-152.         [ Links ]

[4] C. Cowen and B. D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics. Boca Raton, FL: CRC Press. xii, 1995.         [ Links ]

[5] M. Kotilainen, Studies on composition operators and function spaces, Report Series. Department of Mathematics, University of Joensuu 11. (Dissertation) 2007.         [ Links ]

[6] P. Lappan and J. Xiao, #α-bounded composition maps on normal classes, Note di Matematica, 20(1) (2000/2001), 65-72.         [ Links ]

[7] X. Li, On hyperbolic Q classes, Dissertation, University of Joensuu, Joensuu, 2005, Ann. Acad. Sci. Fenn. Math. Diss. 145 (2005), 65 pp.         [ Links ]

[8] X. Li, F. Pérez-González, and J. Rãttyã, Composition operators in hyperbolic Q-classes, Ann. Acad. Sci. Fenn. Math. 31 (2006), 391-404.         [ Links ]

[9] S. Makhmutov and M. Tjani, Composition operators on some Möbius invariant Banach spaces, Bull. Austral. Math. Soc. 62 (2000), 1-19.         [ Links ]

[10] F. Pérez-González, J. Rättyä and J. Taskinen, Lipschitz Continuous and Compact Composition Operators in Hyperbolic Classes, Mediterr. J. Math. 8 (2011), 123-135.         [ Links ]

[11] W. Smith, Inner functions in the hyperbolic little Bloch class, Michigan Math. J. 45(1) (1998), 103-114.         [ Links ]

[12] M. Tjani, Compact composition operators on Besov spaces, Trans. Amer. Math. Soc. 355 (2003), 4683-4698.         [ Links ]

[13] J. Xiao, Holomorphic Q classes, Lecture Notes in Mathematics, 1767, Springer-Verlag, Berlin, 2001.         [ Links ]

[14] S. Yamashita, Hyperbolic Hardy classes and hyperbolically Dirichlet-finite functions, Hokkaido Math. J., Special Issue 10 (1981), 709-722.         [ Links ]

[15] S. Yamashita, Functions with p hyperbolic derivative, Math. Scand. 53 (2)(1983), 238-244.         [ Links ]

[16] S. Yamashita, Holomorphic functions of hyperbolic bounded mean oscillation, Boll. Un. Math. Ital. 5 B(6), (3)(1986), 983-1000.         [ Links ]

[17] J. Zhou, Composition operators from α to K type spaces, J. Funct. Spaces Appl. 6 (1)(2008), 89-105.         [ Links ]

Received: February 2012 / Accepted: November 2012.

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