Which people dwelled in lands peripheral to the Byzantine and Sasanian empires at the time Islam arose?

The Arabs Muslims

Explanation:

Arabs Muslims were the ones who started conquering the neighbor's territories; and within it, were the Byzantine and the Sasanian empires. The Arab Muslim forces took advantage that these territories were weakened by their never-ending fighting with each other. When they conquered the Byzantine and Sasanian territory they started to expand and conquer beyond those lands. The reasons of conquering these lands were majorly political and religious.