A class of integrals with respect to homogeneous Lévy bases on $\mathbb{R}^k$ is considered. In the one-dimensional case $k=1$ this class corresponds to the selfdecomposable distributions. Necessary and sufficient conditions for existence as well as some representations of the integrals are given. Generalizing the one-dimensional case it is shown that the class of integrals corresponds to Urbanik's class $L_{k-1}(\mathbb{R})$. Finally, multiparameter Ornstein-Uhlenbeck processes are defined and studied.

Keywords: Lévy bases; stochastic integrals; Urbanik's classes; multiparameter Ornstein-Uhlenbeck processes.

AMS Subject Classification (2010): 60G51; 60G57; 60H05.