Carleson potentials and the reproducing kernel thesis for embedding theorems

Abstract

In this note we present a new proof of the Carleson Embedding Theorem on the unit disc and unit ball in $\C^n$. The only technical tool used in the proof of this fact is Green's formula. The starting point is that every Carleson measure gives rise to a bounded subharmonic function. Using this function we construct a new related Carleson measure that allows for a simple embedding. In the case of the disc $\D$ this gives the best known constant, with the previous best given by N.~Nikolskii.