Carleson’s Interpolation Theorem Deduced from a Result of Pick

Abstract

The proof of Carleson’s theorem to be given below was worked up in response to a particular teaching situation. About a year and a half ago, I was assigned our department’s first (semester) course on functional analysis, normally devoted to the three principles of that subject and to some of their applications. My class consisted of quite good students with an adequate preparation in measure theory and integration but only a rather scanty knowlege of analytic functions; I desired nevetheless to show them how Carleson’s result could be made to follow from the rudiments of the subject. The problem with this was that the students could not be expected to know anything about H _p spaces or their duality, and class time did not allow for any preliminary discussion of that material.