About the density of spectral measure of the two-dimensional SaS random vector

In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function ${\displaystyle \exp \{-{(\left|a\right|p+\left|b\right|p)}^{\frac{\alpha }{p}}\}}$ is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].