Geodesic
Cesàro Operators on the Hardy Spaces of the Half-Plane
Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 229-240

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2011-153-7
Mots-clés : 47B38, 30H10, 47D03, Cesàro operators, Hardy spaces, semigroups, composition operators 
Arvanitidis, Athanasios G.; Siskakis, Aristomenis G. Cesàro Operators on the Hardy Spaces of the Half-Plane. Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 229-240. doi: 10.4153/CMB-2011-153-7
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