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Similarity to a contraction and hypercontractivity of composition operators |
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| Authors: | Nizar Jaoua |
| Institution: | Department of Mathematics, Université Lille I, Cité Scientifique, F-59655 Villeneuve d'Ascq, France |
| Abstract: | On the Hardy spaces  with  , we consider the composition operators induced by analytic self-maps of the open unit disc  . First, we characterize those which are similar to contractions. Then, we give some necessary and sufficient conditions for them to be hypercontractive. Finally, we prove that, among those ones, only the zero-symbol composition operator sends  into  with a norm less than or equal to  . |
| Keywords: | Composition operators Hardy spaces contraction hypercontractive (or $\beta$-contractive) operator |
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