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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.15 no.3 Temuco  2013

http://dx.doi.org/10.4067/S0719-06462013000300003 

 

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. ahsayed80@hotmail.com

3Department of Mathematics, Faculty of Science, Assiut Branch, Al-Azhar University, Assiut 32861, Egypt. mabakhit2007@hotmail.com


ABSTRACT

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.


RESUMEN

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.


 

References

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Received: February 2012 / Accepted: November 2012.

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