Korean J. Math.  Vol 24, No 4 (2016)  pp.647-662
DOI: 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

A. Kamal, A. El-Sayed Ahmed, T. I. Yassen

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 ${\mathcal{B}}^{*}_{p,\log,\alpha}$ and general hyperbolic Besov-type classes ${F_{p,\log}^{*}(p,q,s)}.$ 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 B∗ p,log,α, the general hyperbolic Besov-type classes F ∗ p,log(p, q, s)..

Subject classification

47B38, 46E15.

Sponsor(s)



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