At the point of this event Satan had dominion over the earth that was given to him by Adam when Adam yielded to temptation and died spiritually. <p>So Satan did have the authority to give Jesus dominion over the earth. Rather than submitting, Jesus gained back that dominion at His resurrection by remaining faithful to  His HolySpiritFather. <p>Upon His ascension Jesus handed that dominion over to the church as His stewards. Since the church has not dominated the earth as He intended, Jesus will take dominion back from the antichrist at His return.