Geodesic
On vector-valued inequalities for Sidon sets and sets of interpolation
Colloquium Mathematicum, Tome 64 (1993) no. 2, pp. 233-244

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Let E be a Sidon subset of the integers and suppose X is a Banach space. Then Pisier has shown that E-spectral polynomials with values in X behave like Rademacher sums with respect to $L_p$-norms. We consider the situation when X is a quasi-Banach space. For general quasi-Banach spaces we show that a similar result holds if and only if E is a set of interpolation ($I_0$-set). However, for certain special classes of quasi-Banach spaces we are able to prove such a result for larger sets. Thus if X is restricted to be "natural" then the result holds for all Sidon sets. We also consider spaces with plurisubharmonic norms and introduce the class of analytic Sidon sets. 
N. Kalton. On vector-valued inequalities for Sidon sets and sets of interpolation. Colloquium Mathematicum, Tome 64 (1993) no. 2, pp. 233-244. doi: 10.4064/cm-64-2-233-244
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