Carleson potentials and the reproducing kernel thesis for embedding theorems
Petermichl, Stefanie ; Treil, Sergei ; Wick, Brett D.
Illinois J. Math., Tome 51 (2007) no. 3, p. 1249-1263 / Harvested from Project Euclid
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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.
Publié le : 2007-10-15
Classification:  32A70,  30D55,  42B30,  46E22 
@article{1258138542,
     author = {Petermichl, Stefanie and Treil, Sergei and Wick, Brett D.},
     title = {Carleson potentials and the reproducing kernel thesis for embedding theorems},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 1249-1263},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138542}
}

Petermichl, Stefanie; Treil, Sergei; Wick, Brett D. Carleson potentials and the reproducing kernel thesis for embedding theorems. Illinois J. Math., Tome 51 (2007) no. 3, pp.  1249-1263. http://gdmltest.u-ga.fr/item/1258138542/