  Curved broad-band spectral distributions of non-thermal sources like blazars
are described well by a log-parabolic (LP) law where the second degree term
measures the curvature. LP energy spectra can be obtained for relativistic
electrons by means of a statistical acceleration mechanism whose probability of
acceleration depends on energy. In this paper we compute the spectra radiated
by an electron population via synchrotron (S) and Synchro-Self Compton(SSC)
processes to derive the relations between the LP parameters. These spectra were
obtained by means of an accurate numerical code. We found that the ratio
between the curvature parameters of the S spectrum to that of the electrons is
equal to about 0.2 instead of 0.25, the value foreseen in the delta
approximation. Inverse Compton spectra are also intrinsically curved and can be
approximated by a log-parabola only in limited ranges. The curvature parameter,
estimated around the SED peak, may vary from a lower value than that of the S
spectrum up to that of emitting electrons depending on whether the scattering
is in the Thomson or in the Klein-Nishina regime. We applied this analysis to
computing the SSC emission from the BL Lac object Mkn 501 during the large
flare of April 1997. We fit simultaneous BeppoSAX and CAT data and reproduced
intensities and spectral curvatures of both components with good accuracy. The
large curvature observed in the TeV range was found to be mainly intrinsic, and
therefore did not require a large pair production absorption against the
extragalactic background. We regard this finding as an indication that the
Universe is more transparent at these energies than previously assumed by
several models found in the literature. This conclusion is supported by recent
detection of two relatively high redshift blazars with H.E.S.S.
