  We construct intrinsic on-and off-diagonal upper and lower estimates for the
transition probability density of a L\'evy process in small time.
  By intrinsic we mean that such estimates reflect the structure of the
characteristic exponent of the process. The technique used in the paper relies
on the asymptotic analysis of the inverse Fourier transform of the respective
characteristic function. We provide several examples, in particular, with
rather irregular L\'evy measure, to illustrate our results.
