My bike (a KTM Duke 200) has poor acceleration at low engine speed (from 2000 to 4000 rpm) in every gear, but after 4000 rpm is the acceleration is normal.
What could the problem be?
What you are describing is not a problem. That is how internal combustion engines works.
The torque/hp of the engine is not constant across the RPM band. My guess is that your peak torque is after 4000RPM for that particular engine, which is why you feel like acceleration is lower when the RPM is below 4000. I'm not an expert in this subject, but check out the answers for the following question for more details: What is the difference between torque and horsepower?
Note: This is assuming the behaviour has not gotten worse recently compared to what it was from out of the factory.