Three upsilon transforms related to tempered stable distributions

We discuss the properties of three upsilon transforms, which are related to the class of p-tempered alpha-stable (T S-alpha(p)) distributions. In particular, we characterize their domains and show how they can be represented as compositions of each other. Further, we show that if -infinity < beta < alpha < 2 and 0 < q < p < infinity then they can be used to transform the Levy measures of T S-beta(p) distributions into those of T S-alpha(q).