  In this paper, we study the existence of the transition densities of
one-dimensional L\'evy processes. Compared with past results, our results
contain the L\'evy processes whose L\'evy symbols have logarithm behavior at
infinity. Our results contain the L\'evy symbol induced by the following
Laplace exponent
  $\psi(\xi) := (\ln(1 + \ln(1 + \ln(\cdots \ln(1 + |\xi|)))))^\epsilon$ ($n$
times), $0 < \epsilon < 1$, $2 \le n$.
  We also show that $\psi(\xi)$ is a L\'evy symbol with transition density.
