CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Cesàro Operators on the Hardy Spaces of the Half-Plane

  Published:2011-08-03
 Printed: Jun 2013
  • Athanasios G. Arvanitidis,
    Department of Mathematics, University of Thessaloniki, 54124 Thessaloniki, Greece
  • Aristomenis G. Siskakis,
    Department of Mathematics, University of Thessaloniki, 54124 Thessaloniki, Greece
Format:   LaTeX   MathJax   PDF  

Abstract

In this article we study the Cesàro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta, $$ 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 Ces\`{a}ro operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also discussed.
Keywords: Cesàro operators, Hardy spaces, semigroups, composition operators Cesàro operators, Hardy spaces, semigroups, composition operators
MSC Classifications: 47B38, 30H10, 47D03 show english descriptions Operators on function spaces (general)
Hardy spaces
Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}
47B38 - Operators on function spaces (general)
30H10 - Hardy spaces
47D03 - Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/