Cesaro operators on the Hardy spaces of the half-plane

2010/06/08 by Arvanitidis, Athanasios G., Siskakis, Aristomenis G. · 1 citation
#47B38 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1006.1520

Abstract

In this article we study the Cesàro operator C(f)(z)=(1)/(z)∫₀^zf(ζ) dζ, and its companion operator T on Hardy spaces of the upper half plane. We identify C and T as resolvents for appropriate semigroups of composition operators and we find the norm and the spectrum in each case. The relation of C and T with the corresponding Cesàro operators on Lebesgue spaces L^p(\R) of the boundary line is also discussed.

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