Asymptotic behaviour of the distribution density of some Lévy functionals in $\mathbb{ R}^n$

The paper is devoted to the asymptotic behaviour of the distribution density of some Lévy functionals in $\mathbb{R}^n$. We generalize the results obtained in [18] for the case when $\theta(t)+ \|x\|\to\infty$, where $\theta(t)$ is some "scaling" function, and $(t,x)$ belong to a suitable domain of $\mathbb{R}_+\times \mathbb{R}^n$.