Carleson for Beginners

Abstract

When I was just beginning as a research student, an older mathematical friend invited me to dine at Trinity. At dessert I was seated next to Littlewood, Hardy’s collaborator and a legendary figure in modern British analysis. With old fashioned politeness, Littlewood set himself out to entertain me. He talked about a recent comet and recalled how fifty years earlier he had viewed Halley’s comet in company with a Trinity fellow who had himself seen its previous visitation. He then spoke about Carleson’s recent proof of the convergence theorem, what a marvellous result it was, how surprising it was that it turned out that Lusin’s conjecture was true, how many people known to him had thought about the problem for a long time without success and how much he regretted being too old to take up the task of understanding the details of the proof.