  Very high energy (VHE) gamma-ray emission from a distant source (z >~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. 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 (g >~ 10^3, E=g 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. To
test our estimation methods, we use the observations of two blazars with
exceptionally hard spectral indices (alpha <~ 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.
