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6 Studia Mathematica

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On the embedding of 2-concave Orlicz spaces into L¹

100%

Schütt C.

nr 1

73-80

In [K-S 1] it was shown that $Ave_π(∑_{i=1}^{n} |x_i a_{π(i)}|^2)^{1/2}$ is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence $a_1,...,a_n$ so that the above expression is equivalent to a given Orlicz norm.

Combinatorial inequalities and subspaces of L₁

63%

Prochno J. , Schütt C.

2012

tom 211

nr 1

21-39

Let M₁ and M₂ be N-functions. We establish some combinatorial inequalities and show that the product spaces $ℓⁿ_{M₁}(ℓⁿ_{M₂})$ are uniformly isomorphic to subspaces of L₁ if M₁ and M₂ are "separated" by a function $t^{r}$, 1 < r < 2.

Approximation of the Euclidean ball by polytopes

51%

Ludwig M. , Schütt C. , Werner E.

nr 1

1-18

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 $volₙ(B₂ⁿ△ P) ≤ c volₙ(B₂ⁿ)N^{-2/(n-1)}$ where B₂ⁿ denotes the Euclidean unit ball of dimension n.

Some combinatorial and probabilistic inequalities and their application to Banach space theory II

51%

Kwapień S. , Schütt C.

nr 2

141-154

On the Banach-Mazur distance of finite-dimensional symmetric Banach spaces and the hypergeometric distribution

50%

Schütt C.

nr 2

109-129

On the positive projection constant

26%

Schütt C.

nr 2

185-198