Many scholars doubt that the epistles in the New Testament named after James, Jude and Peter were actually written by those individuals. There is some logic to that doubt. After all, James, Jude and Peter were all blue collar Galileans with no formal education. Yet the Greek and the rhetorical skill found in these letters is far above what you would expect from such men. For many scholars that is enough to close the case against traditional authorship.
However, I think this is making an unfortunate assumption. It is true that if you handed a parchment to James, Jude and Peter in the early 30′s, you probably would not have gotten the quality of epistle, especially in Greek, that we have in the New Testament. But these letters were not written in the early 30′s. Nor were they written in the context of a blue collar occupation. These men had a number of decades of high level church leadership. James and Paul were the top leaders of the church, and Jude was likely up there as well. They wrote, not as fisherman or carpenters, but as experienced communicators. They likely had some basic Greek even when they lived in Galilee. We know from Acts that from very early (even before the Gentiles joined the church), there was a significant Greek part of the church. It would have been in their best interest to learn Greek and just because one is blue collar, does not mean there is lack of intelligence in gaining language skills.
Even so, could they really have written such good Greek? Remember, these are the top leaders of the church. Surely there would be significant resources that went along with that role. There would have been people skilled in the Greek language that could have polished the language of these letters, while retaining the message. We know from Paul’s letters that he used others in the actual writing of his letters. It is likely the same with these other three writers. When one takes into account the timing and the role of the authors, I see no reason not to accept the traditional authorship of James, Jude and 1 & 2 Peter.