We discuss the properties of three upsilon transforms, which are related to the class of $p$-tempered $\alpha$-stable ($TS^p_\alpha$) distributions. In particular, we characterize their domains and show how they can be represented as compositions of each other. Further, we show that if $-\infty<\beta<\alpha<2$ and $0<q<p<\infty$ then they can be used to transform the Lévy measures of $TS^p_\beta$ distributions into those of $TS^q_\alpha$.
"Three upsilon transforms related to tempered stable distributions." Electron. Commun. Probab. 20 1 - 10, 2015. https://doi.org/10.1214/ECP.v20-4366