Quite popular in the East. But I'm not sure how to answer your 'influence' question. One of the reason the Areopagite's corpus is popular in the East is that it's seen as representative of the entire underlying tradition. I mean the Areopagite's words on apohatic theology, the unknowability of God, are often quoted in Eastern theology texts--but unless he actually is St. Dionysius the Areopagite, he didn't invent the concept, its to be found in the highly influential Cappadocian fathers well before the assumed date of the Areopagite corpus' composition. The Areopagite simply did an excellent job of conveying it.