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math.FA2010★ 36 cited
Maximal theorems and square functions for analytic operators on Lp-spaces
Christian Le Merdy, Quanhua Xu
Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for…
math.FA2010
Gamma-bounded representations of amenable groups
Christian Le Merdy
Let G be an amenable group, let X be a Banach space and let π: G --> B(X) be a bounded representation. We show that if the set {π(t) : t \in G} is gamma-bounded then πextends to a…