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

DOI

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
@article{10_4153_CMB_2011_153_7,
     author = {Arvanitidis, Athanasios G. and Siskakis, Aristomenis G.},
     title = {Ces\`aro {Operators} on the {Hardy} {Spaces} of the {Half-Plane}},
     journal = {Canadian mathematical bulletin},
     pages = {229--240},
     year = {2013},
     volume = {56},
     number = {2},
     doi = {10.4153/CMB-2011-153-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-153-7/}
}
TY  - JOUR
AU  - Arvanitidis, Athanasios G.
AU  - Siskakis, Aristomenis G.
TI  - Cesàro Operators on the Hardy Spaces of the Half-Plane
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 229
EP  - 240
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-153-7/
DO  - 10.4153/CMB-2011-153-7
ID  - 10_4153_CMB_2011_153_7
ER  - 
%0 Journal Article
%A Arvanitidis, Athanasios G.
%A Siskakis, Aristomenis G.
%T Cesàro Operators on the Hardy Spaces of the Half-Plane
%J Canadian mathematical bulletin
%D 2013
%P 229-240
%V 56
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-153-7/
%R 10.4153/CMB-2011-153-7
%F 10_4153_CMB_2011_153_7

Cité par Sources :