a1 Texas A. and M. University and Equipe D'Analyse, Université; Paris VI, Tour 46 –4ème Etage, 4, Place Jussieu, 75252 –; Paris Cedex 05
We prove the result in the title. More generally we consider the Banach space υp, of all sequences (xn) of scalars such that
where the supremum runs over all increasing sequences n1 ≤ n2 ≤ …. We show that is of cotype 2 if p 2 and of cotype p′, where 1/p′ + 1/p = 1, if p ≤ 2. Similar results are obtained for the analogous function spaces.
(Received May 25 1987)