Does Amati Relation Depend on Luminosity of GRB's Host Galaxies?

In order to test systematic of the Amati relation, the 24 long-duration GRBs with firmly determined $E_{\gamma ,\mathrm{i}\mathrm{s}\mathrm{o}}$ and $E_{\mathrm{p}}$ are separated into two sub-groups according to B-band luminosity of their host galaxies. The Amati relations in the two subgroups are found to be in agreement with each other within uncertainties. Taking into account of the well established luminosity - metallicity relation of galaxies, no strong evolution of the Amati relation with GRB’s environment metallicity is implied in this study.