Mrk 421, Mrk 501, and PKS 2344+514 are all at z < 0.05, which is the lower limit for the analytic approximation given in Stecker & Scully (2006): this, although it means slightly overestimating the (modest) true absorption for these sources, will in no way affect the main conclusions of this paper.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

The full-band k-correction, to be applied to the 2-10 keV luminosities and the 0.2-2 TeV luminosities, amounts to a factor $(1+z)^{\Gamma-2}$ if in the relavant band the spectrum is power law with intrinsic slope $\Gamma$ . For the blazars in Table 1, it is either z < 0.1 or $\alpha_\gamma^{\rm corr}$ $\sim$ 2 (and typically $\alpha_{2-10~{\rm keV}}$ $\sim$ 2.2, see Donato et al. 2005), so the corresponding k-corrections to the X-ray and VHE ${\gamma}$ -ray luminosities are small.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.