The A318 doesn't have the range to go transatlantic (without a westbound fuel stop) unless you're talking about something like SNN
. The "A319" which PrivatAir uses is an A319LR (predecessor of the ACJ, if I'm not mistaken) with extra fuel capacity, and, as others have said, it's configured as all-business class to help keep the weight down. Same for the "737" they operate, which is really a BBJ
(-700 with the strengthened -800 wing and extra fuel tanks).
The problem with operating these all-business-class transatlantic flights is that they can easily steal premium traffic from the operator's existing widebody services unless used on niche routes which would not otherwise be operated. And in general, these flights need corporate contracts with guaranteed seat purchases to generate reliable profits.
Not only are bizjets more luxurious for transatlantic travel, they also offer the high-end passenger the ability to avoid most of the inconveniences associated with international travel -- no 60/90-minute check-in, no security screening lines, no boarding lounge filled with 400 people including crying babies, separate immigration/customs facilities on arrival, no connections required, etc.