Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual bounded sequence in , then is a Carleson measure, which gives a short proof in one variable of a theorem of L. Carleson and in several variables of a theorem of P. Thomas.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-6,
author = {Eric Amar},
title = {Interpolating sequences, Carleson measures and Wirtinger inequality},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {79-87},
zbl = {1145.32001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-6}
}
Eric Amar. Interpolating sequences, Carleson measures and Wirtinger inequality. Annales Polonici Mathematici, Tome 93 (2008) pp. 79-87. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-6/