# Fourier transform pair for $ln(ln(…))$ cascade?

I need to analyze real signals $$y_i$$ in the frequency domain. $$y_i$$ are defined like:

$$y_1 = ln(ln(x))$$

$$y_2 = ln(ln(ln(x)))$$

$$y_3 =~ ...$$

$$...$$

Are there Fourier transformation pairs for this kind of problem? $$x$$ is real and non-negative.

• Why not apply an equal number of $e$ exponentiations to get rid of the $\ln$ (?) – A_A Apr 10 at 9:15