Cesàro Operators on the Hardy Spaces of the Half-Plane

Canadian mathematical bulletin

Aristomenis G. Siskakis¹  Athanasios G. Arvanitidis¹ 

[1] Department of Mathematics, University of Thessaloniki, 54124 Thessaloniki, Greece

关键词: Cesàro operators;    Hardy spaces;    semigroups;    composition operators;   

DOI  :  10.4153/CMB-2011-153-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this article we study the Cesàrooperator$$mathcal{C}(f)(z)=frac{1}{z}int_{0}^{z}f(zeta),dzeta,$$ and its companion operator $mathcal{T}$ on Hardy spaces of theupper half plane. We identify $mathcal{C}$ and $mathcal{T}$ asresolvents for appropriate semigroups of composition operators and wefind the norm and the spectrum in each case. The relation of$mathcal{C}$ and $mathcal{T}$ with the corresponding Ces`{a}rooperators on Lebesgue spaces $L^p(mathbb R)$ of the boundary line is alsodiscussed.

【 授权许可】

Unknown