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Cesàro Operators on the Hardy Spaces of the Half-Plane

Published online by Cambridge University Press:  20 November 2018

Athanasios G. Arvanitidis  and
Aristomenis G. Siskakis
Athanasios G. Arvanitidis
Affiliation:
Department of Mathematics, University of Thessaloniki, 54124 Thessaloniki, Greece e-mail: [email protected]@math.auth.gr
Aristomenis G. Siskakis
Affiliation:
Department of Mathematics, University of Thessaloniki, 54124 Thessaloniki, Greece e-mail: [email protected]@math.auth.gr
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Abstract

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In this article we study the Cesàro operator

$$C\left( f \right)\left( Z \right)=\frac{1}{Z}\int_{0}^{Z}{f\left( \zeta \right)d}\zeta,$$

and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as resolvents for appropriate semigroups of composition operators and we find the norm and the spectrum in each case. The relation of $\mathcal{C}$ and $\mathcal{T}$ with the corresponding Cesàro operators on Lebesgue spaces ${{L}^{p}}\left( \mathbb{R} \right)$ of the boundary line is also discussed.

Keywords

47B3830H1047D03Cesàro operatorsHardy spacessemigroupscomposition operators
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 2 , 01 June 2013 , pp. 229 - 240
Copyright
Copyright © Canadian Mathematical Society 2013

References

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