The Arabs have assiduously propagated the myths that Jerusalem is an Arab capital, that (after Mecca and Medina) Jerusalem is their third holy city, and that it is intolerable to them that infidels (Jews) are in possession of it.
The reality of course is that Jerusalem was never an Arab capital and that it was, until the Jews revitalized it, a dusty provincial city that hardly played any economic, social, or political role. Jerusalem is mentioned hundreds of times in the Jewish Bible and has been the center of the Jewish faith and the focus of Jewish longing ever since the Romans destroyed the Temple in the early years of the first millennium. Not once is Jerusalem mentioned in the Koran.
As to “East Jerusalem”: There is East Saint Louis, there is East Hampton, and there used to be East Berlin, but, until the Arab propaganda machine created the concept, there was never in history an “East Jerusalem”, let alone an “Arab East Jerusalem”.
The eastern part of Jerusalem is now predominantly inhabited by Arabs, though their proportion is decreasing. But what is the reason for this? It is because the Jordanians destroyed all traces of Jewish presence from the eastern part of the city and drove all the Jews out during the 19 years (between 1948 and 1967) in which they were in occupation of the eastern part of the city. The world, informed by Arab propaganda, considers those Jews who wish to return to the eastern part of the city to be troublemakers or worse.
The concept of Jerusalem being a holy Arab city and the capital of whatever political entity the “Palestinians” may eventually form is a myth and so of course is the concept of “Arab East Jerusalem”.