INEQUALITIES BETWEEN INTEGRALS OF 
-STABLE SYMMETRIC
MEASURES ON BANACH SPACES
Abstract: Let 
and 
be symmetric Gaussian probability measures on a Banach space 
and let 
be the dual of 
Then, as is well known, the inequality
implies
If
we replace Gaussian measures by
-stable ones (
), the property does not hold.
Thus we consider the class
of such Banach spaces, where a generalization to the
-stable case is true. Furthermore, we give relations of
to some other classes of Banach
spaces and we get also inclusion properties of
Recently, similar classes of
Banach spaces have been investigated by Mandrekar, Thang, Tien, and Weron.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -
