Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 8, Number 1 (2014), 118-137.
New estimate of essential norm of composition followed by differentiation between Bloch-type spaces
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.
Banach J. Math. Anal., Volume 8, Number 1 (2014), 118-137.
First available in Project Euclid: 14 October 2013
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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