In [K-S 1] it was shown that is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence so that the above expression is equivalent to a given Orlicz norm.
Let M₁ and M₂ be N-functions. We establish some combinatorial inequalities and show that the product spaces are uniformly isomorphic to subspaces of L₁ if M₁ and M₂ are “separated” by a function , 1 < r < 2.
There is a constant c such that for every n ∈ ℕ, there is an Nₙ so that for every N≥ Nₙ there is a polytope P in ℝⁿ with N vertices and where B₂ⁿ denotes the Euclidean unit ball of dimension n.
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