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.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 24th May 2017. This data will be updated every 24 hours.