Compact composition operators on $H^2$ and Hardy-Orlicz spaces

Details Compact composition operators on $H^2$ and Hardy-Orlicz spaces Compact composition operators on $H^2$ and Hardy-Orlicz spaces

2008-06-25

arxiv.org/abs/0806.4206v1

Mathematics

Functional Analysis

17 pages

Scientific paper

We compare the compactness of composition operators on $H^2$ and on
Orlicz-Hardy spaces $H^\Psi$. We show in particular that exists an Orlicz
function $\Psi$ such that $H^{3+\eps} \subseteq H^\Psi \subseteq H^3$ for every
$\eps >0$, and a composition operator $C_\phi$ which is compact on $H^3$ and on
$H^{3+\eps}$, but not compact on $H^\Psi$.

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