  In this paper we determine the Fourier series expansion of the log-Barnes
function. This is the analogue of the classical result of Kummer and Malmsten.
  Applying this expansion we get some integrals similar to the Espinosa-Moll
log-Gamma integrals with respect to $\log G$. During the course of the paper
some interesting log-Gamma integrals and a log-harmonic sum are evaluated.
