Context :

Aims : Very high energy ( VHE ) gamma-ray emission from a distant source ( z \gtrsim 0.2 ) can be efficiently absorbed my means of the electron-positron pair creation process .
Analyses of the unabsorbed spectra imply that the intrinsic TeV emission of some blazars is hard , with spectral indices 0.5 < \alpha < 1 .
The absorption depends on the level of extragalactic background light ( EBL ) that is difficult to measure directly .
This implies that it is difficult to estimate the slope of the intrinsic TeV emission .
To test our blazar emission scenario that is capable to reproducing the hard spectra , we therefore used the observations made by the Fermi Gamma-ray Space Telescope in the unabsorbed MeV-GeV energy range .

Methods : We assume that the X-ray and gamma-ray emission of TeV blazars is produced in a compact region of a jet uniformly filled by particles of relatively high energy ( \gamma \gtrsim 10 ^ { 3 } ,E = \gamma m _ { e } c ^ { 2 } ) .
In other words , we assume a low energy cut-off in the particle energy distribution .
The emission produced by the particles with this energy spectrum can explain hard intrinsic spectra in the energy range from MeV up to TeV .
We demonstrate how to estimate the basic physical parameters of a source in this case and how to explain the observed spectra by a precise simulation of the particle energy evolution .

Results : To test our estimation methods , we use the observations of two blazars with exceptionally hard spectral indices ( \alpha \lesssim 0.5 ) in the MeV-GeV range and known redshifts : RGB J0710+591 and 1ES 0502+675 .
The estimated values of the Doppler factor and magnetic field are compared with our numerical simulations , which confirm that the particle energy distribution with a low energy cut–off can explain the observed hard spectra well .
In addition , we demonstrate that the radiative cooling caused by the inverse-Compton emission in the Klein-Nishina regime may help us to explain the hard spectra .

Conclusions :