The atmospheric pressure discharge in an air gap between two dielectric barrier electrodes has been studied experimentally and the development of an electron avalanche in such an air gap was simulated numerically. The results show that, while it is possible to obtain glow discharge in an air gap not longer than 2 mm, the streamer discharge could only be obtained in an air gap longer than 5 mm if no methods could be used to lower the electric field when discharging. The "iontrapping mechanism", which was said to be responsible for the atmospheric pressure glow discharge, was not verified in the experiments.