Is an expiatory offering (kaffarah) for an oath (yamin) obligatory upon someone who swore not to read anything to his friend unless his friend read what the swearer had written, and then the swearer was compelled to break his oath, keeping in mind that he does not remember whether he was an adult at the time of the oath or not?

If you are not certain that you reached the age of maturity at the time of the oath, then there is nothing upon you. However, if you are certain of it and you broke your oath – by reading what your friend wrote for you before he read what you wrote for him – then expiation is incumbent upon you. It is worth noting that the Shafi'is hold the view that there is no breach of the oath if he read it before you became aware of that, and then you read it to him. The more cautious approach is to offer expiation for the oath if you are certain that you reached the age of accountability at the time of the oath.