Tensor products for Gelfand-Shilov and Pilipovi{\'c} distribution spaces

We show basic properties on tensor products for Gelfand-Shilov distributions and Pilipovi{'c} distributions. This also includes the Fubbini’s property of such tensor products. We also apply the Fubbini property to deduce some properties for short-time Fourier transforms of Gelfand-Shilov and Pilipovi{'c} distributions.