[alpha]-Stable characterization of Banach spaces (1 < [alpha] < 2)

This work characterizes some subclasses of [alpha]-stable (0 < [alpha] < 1) Banach spaces in terms of the extendibility to Radon laws of certain [alpha]-stable cylinder measures. These result extend the work of S. Chobanian and V. Tarieladze (J. Multivar. Anal.7, 183-203 (1977)). For these spaces it is shown that every Radon stable measure is the continuous image of a stable measure on a suitable L[beta] space with [beta] = [alpha](1 - [alpha])-1. The latter result extends some work of Garling (Ann. Probab.4, 600-611 (1976)) and Jain (Proceedings, Symposia in Pure Math. XXXI, p. 55-65, Amer. Math. Soc., Providence, R.I.).