Geodesic
On the type constants with respect to systems of characters of a compact abelian group
Studia Mathematica, Tome 118 (1996) no. 3, pp. 231-243

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We prove that there exists an absolute constant c such that for any positive integer n and any system Φ of $2^n$ characters of a compact abelian group, $2^{-n/2} t_Φ(T) ≤ c n^{-1/2} t_n(T)$, where T is an arbitrary operator between Banach spaces, $t_Φ(T)$ is the type norm of T with respect to Φ and $t_n(T)$ is the usual Rademacher type-2 norm computed with n vectors. For the system of the first $2^n$ Walsh functions this is even true with c=1. This result combined with known properties of such type norms provides easy access to quantitative versions of the fact that a nontrivial type of a Banach space implies finite cotype and nontrivial type with respect to the Walsh system or the trigonometric system. 
Aicke Hinrichs. On the type constants with respect to systems of characters of a compact abelian group. Studia Mathematica, Tome 118 (1996) no. 3, pp. 231-243. doi: 10.4064/sm-118-3-231-243
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