Banach Journal of Mathematical Analysis

New estimate of essential norm of composition followed by differentiation between Bloch-type spaces

Yu-Xia Liang and Ze-Hua Zhou

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Abstract

We give a new characterization for the boundedness of composition operator followed by differentiation operator acting on Bloch-type spaces and calculate its essential norm in terms of the $n$-th power of the induced analytic self-map on the unit disk. From which some sufficient and necessary conditions of compactness of the operator follow immediately.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 1 (2014), 118-137.

Dates
First available in Project Euclid: 14 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1381782092

Digital Object Identifier
doi:10.15352/bjma/1381782092

Mathematical Reviews number (MathSciNet)
MR3161687

Zentralblatt MATH identifier
1323.47041

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 47B33: Composition operators

Keywords
Bloch-type space composition operator differentiation essential norm

Citation

Liang, Yu-Xia; Zhou, Ze-Hua. New estimate of essential norm of composition followed by differentiation between Bloch-type spaces. Banach J. Math. Anal. 8 (2014), no. 1, 118--137. doi:10.15352/bjma/1381782092. https://projecteuclid.org/euclid.bjma/1381782092


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