Carleson Potentials and the Reproducing Kernel Thesis for Embedding Theorems

Details Carleson Potentials and the Reproducing Kernel Thesis for Embedding Theorems Carleson Potentials and the Reproducing Kernel Thesis for Embedding Theorems

2007-01-29

arxiv.org/abs/math/0701851v1

Illinois J. Math. 51 (2007), no. 4, 1249--1263

Mathematics

Classical Analysis and ODEs

11 pages, to appear in Illinois Journal of Mathematics

Scientific paper

In this note we present a new proof of the Carleson Embedding Theorem on the unit disc and unit ball. 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 this gives the best known constant, with the previous best given by N. Nikolskii.

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