  We calculate the dynamical spin-spin correlation functions of a Kondo dot
coupled to two noninteracting leads held at different chemical potentials. To
this end we generalize a recently developed real-time renormalization group
method in frequency space (RTRG-FS) to allow the calculation of dynamical
correlation functions of arbitrary dot operators in systems describing spin
and/or orbital fluctuations. The resulting two-loop RG equations are
analytically solved in the weak-coupling regime. This implies that the method
can be applied provided either the voltage $V$ through the dot or the external
magnetic field $h_0$ are sufficiently large, $\max\{V,h_0\}\gg T_K$, where the
Kondo temperature $T_K$ is the scale where the system enters the
strong-coupling regime. Explicitly, we calculate the longitudinal and
transverse spin-spin correlation and response functions as well as the
resulting fluctuation-dissipation ratios. The correlation functions in
real-frequency space can be calculated in Matsubara space without the need of
any analytical continuation. We obtain analytic results for the line-shape, the
small- and large-frequency limits and several other features like the height
and width of the peak in the transverse susceptibility at
$\Omega\approx\tilde{h}$, where $\tilde{h}$ denotes the reduced magnetic field.
Furthermore, we discuss how the developed method can be generalized to
calculate dynamical correlation functions of other operators involving
reservoir degrees of freedom as well.
