as you don't mention a check engine light then this sounds like a lack of fuel and could be a lack of fuel pressure from the electrical pump at the tank.1st thing to try is to remove the fuel filler cap and then flick the ignition on whilst listening for the brief ‘buzz’ of the pump
If the connections to the pump are corroded or damaged then the pump could stop at any time or could not be running at full speed. Check that its relay switches in and out and the relay contacts are clean and bright – replace the relay if in any doubt and do the same for the fuse,Ideally measure the pressure at the injector rail (should usually be around 3Bar / 45psi +) and if this is low check the pump as described and also consider changing the fuel filter as if this partially blocked this too will reduce pressure.
if the power is OK above 4krpm
then I'd suspect that there may be an issue with either the turbocharger or a faulty cam phaser
I'd suggest the next step is to get the car plugged into a scan tool thats capable of monitoring the boost pressure and cam timing so you can see if the engine is following its target parameters or if they are stuck