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The Essential Norm of a Bloch-to-${{Q}_{p}}$ Composition Operator

Published online by Cambridge University Press:  20 November 2018

Mikael Lindstróm ,
Shamil Makhmutov  and
Jari Taskinen
Mikael Lindstróm
Affiliation:
Department of Mathematics Åbo Akademi University FIN-20500 Åbo Finland, e-mail: mlindstr@abo.fi
Shamil Makhmutov
Affiliation:
Department of Mathematics College of Science Sultan Qaboos University PO Box 36 Al-Khod, PC 123 Sultanate of Oman, e-mail: makhm@squ.edu.om
Jari Taskinen
Affiliation:
Department of Mathematics University of Joensuu FIN-80101 Joensuu Finland, e-mail: jari.taskinen@joensuu.fi
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Abstract

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The ${{Q}_{p}}$ spaces coincide with the Bloch space for $p\,>\,1$ and are subspaces of $\text{BMOA}$ for $0\,<\,p\,\le \,1$. We obtain lower and upper estimates for the essential norm of a composition operator from the Bloch space into ${{Q}_{p}}$, in particular from the Bloch space into $\text{BMOA}$.

Keywords

47B3847B1046E4046E15Bloch spacelittle Bloch spaceBMOAVMOAQp spacescomposition operatorcompact operatoressential norm

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 1 , 01 March 2004 , pp. 49 - 59
Copyright
Copyright © Canadian Mathematical Society 2004

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