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October 2020 Properties of $\beta$-Cesàro operators on $\alpha$-Bloch space
Shankey Kumar, Swadesh Kumar Sahoo
Rocky Mountain J. Math. 50(5): 1723-1746 (October 2020). DOI: 10.1216/rmj.2020.50.1723

Abstract

For each α>0, the α-Bloch space consists of all analytic functions f on the unit disk satisfying sup|z|<1(1|z|2)α|f(z)|<+. We consider the following complex integral operators, namely the β-Cesàro operator

C β ( f ) ( z ) = 0 z f ( w ) w ( 1 w ) β d w

and its generalization, acting from the α-Bloch space to itself, where f(0)=0 and β. We investigate the boundedness and compactness of the β-Cesàro operators and their generalizations. Also we calculate the essential norm and spectrum of these operators.

Citation

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Shankey Kumar. Swadesh Kumar Sahoo. "Properties of $\beta$-Cesàro operators on $\alpha$-Bloch space." Rocky Mountain J. Math. 50 (5) 1723 - 1746, October 2020. https://doi.org/10.1216/rmj.2020.50.1723

Information

Received: 1 September 2018; Accepted: 5 March 2020; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274830
MathSciNet: MR4170682
Digital Object Identifier: 10.1216/rmj.2020.50.1723

Subjects:
Primary: 30H30, 46B50, 47B38
Secondary: ‎30H05, ‎45P05‎, 46B25

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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