ere’s some commentary from the New American Bible (Revised Edition):

These “superapostles”: this term, employed again in 2 Cor 12:11b, designates the opponents of whom Paul has spoken in 2 Cor 10 and again in 2 Cor 11:4. They appear to be intruders at Corinth. Their preaching is marked at least by a different emphasis and style, and they do not hesitate to accept support from the community. Perhaps these itinerants appeal to the authority of church leaders in Jerusalem and even carry letters of recommendation from them. But it is not those distant leaders whom Paul is attacking here. The intruders are “superapostles” not in the sense of the “pillars” at Jerusalem (Gal 2), but in their own estimation. They consider themselves superior to Paul as apostles and ministers of Christ, and they are obviously enjoying some success among the Corinthians. Paul rejects their claim to be apostles in any superlative sense (hyperlian), judging them bluntly as “false apostles,” ministers of Satan masquerading as apostles of Christ (2 Cor 11:13–15). On the contrary, he himself will claim to be a superminister of Christ (hyper egō, 2 Cor 11:23). So these “Apostles” are actually not Peter, James, and John. It definitely would make less sense if James was preaching with success in the Gentile city of Corinth especially after Paul’s first letter to the Corinthian community which apparently faced some criticism. At any rate, James would expectantly stay in Jerusalem as Paul continued to preach to the Gentiles like he did to the Galatians.