Chevet's theorem for stable processes. II (Q1112410)

Let B be a separable Banach space and let \(\{\) \(\xi\) : \(| \xi | \leq 1\}\) denote the unit ball of \(B^*\). Let X be a symmetric p-stable B-valued random variable and let \(\{X_ j\}^ n_{j=1}\) be i.i.d. copies of X. Let \(B_ 1\) be a finite-dimensional Banach space with a symmetric unconditional basis \(\{y_ j\}^ n_{j=1}\). An upper bound is obtained for E \(\sup_{| \xi | \leq 1}\| \sum^{n}_{j=1}\xi (X_ j)y_ j\|\) that improves the one given by \textit{E. Giné}, \textit{M. B. Marcus} and \textit{J. Zinn} [in the preceding paper reviewed above, Zbl 0659.60007].