  We present statistics of velocity fluctuations in both the Lagrangian and
Eulerian frame for weakly driven two-dimensional turbulence. We find that
simultaneous inverse energy and enstrophy ranges present in the Lagrangian and
Eulerian Fourier spectra are not directly echoed in real-space moments of
velocity difference. The spectral ranges, however, do line up very well with
ratios of the real-space moments {\em local} exponents, indicating that though
the real-space moments are not scaling ``nicely'', the relative behavior of the
velocity difference probability distribution functions is changing over very
short ranges of length scales. Utilizing this technique we show that the ratios
of the local exponents for Eulerian moments in weak two-dimensional turbulence
behave in agreement with Kolmogorov predictions over the spectrally identified
ranges. The Lagrangian local exponent ratios, however, behave in a different
manner compared to their Eulerian counterparts, and deviate significantly from
what would be expected from Kolmogorov predictions.
