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http://dx.doi.org/10.11568/kjm.2016.24.4.647

LIPSCHITZ CONTINUOUS AND COMPACT COMPOSITION OPERATOR ACTING BETWEEN SOME WEIGHTED GENERAL HYPERBOLIC-TYPE CLASSES  

Kamal, A. (Department of Mathematics Port Said University)
El-Sayed Ahmed, A. (Mathematics Department Sohag University)
Yassen, T.I. (Department of Mathematics Port Said University)
Publication Information
Korean Journal of Mathematics / v.24, no.4, 2016 , pp. 647-662 More about this Journal
Abstract
In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.
Keywords
metric space; the general hyperbolic Bloch-type classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$; the general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}(p,q,s)$;
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