Norm of a composition operator from the space of Cauchy transforms into Zygmund-type spaces

  • Ajay K. Sharma Central Univ. Jammu, (Bagla), Raya-Suchani, Samba, India)
Keywords: composition operator, space of Cauchy transforms, Zygmund-type space, little Zygmund-type space

Abstract

The problem of evaluation of the norm of a composition operator acting between the spaces of holomorphic functions is quite difficult.
In the Hardy and weighted Bergman spaces, the norm of the composition operator is unknown even for the choice of a fairly simple symbol.
We compute the operator norm of composition operator acting between the space of Cauchy transforms and Zygmund-type spaces.
We also characterize bounded and compact composition operators acting between these spaces.



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Published
25.12.2019
How to Cite
SharmaA. K. “Norm of a Composition Operator from the Space of Cauchy Transforms into Zygmund-Type Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 12, Dec. 2019, pp. 1699-11, http://umj.imath.kiev.ua/index.php/umj/article/view/367.
Section
Research articles