  We consider logarithmic extensions of the correlation and response functions
of scalar operators for the systems with aging as well as Schr\"odinger
symmetry. Aging is known to be the simplest nonequilibrium phenomena, and its
physical significances can be understood by the two-time correlation and
response functions. Their logarithmic part is completely fixed by the bulk
geometry in terms of the conformal weight of the dual operator and the dual
particle number.
  Motivated by recent experimental realizations of Kardar-Parisi-Zhang
universality class in growth phenomena and its subsequent theoretical extension
to aging, we investigate our two-time correlation functions out of equilibrium,
which show several qualitatively different behaviors depending on the
parameters in our theory. They exhibit either growing or aging, i.e. power-law
decaying, behaviors for the entire range of our scaling time. Surprisingly, for
some parameter ranges, they exhibit growing at early times as well as aging at
later times.
