Interpolating sequences, Carleson measures and Wirtinger inequality

Eric Amar. "Interpolating sequences, Carleson measures and Wirtinger inequality." Annales Polonici Mathematici 94.1 (2008): 79-87. <http://eudml.org/doc/280383>.

@article{EricAmar2008,
abstract = {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 $μ_\{S\}:= ∑_\{a∈S\} (1-|a|²)ⁿ δ_\{a\}$ 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 $μ_\{S\}$ 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 $H^\{p\}()$, then $μ_\{S\}$ 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.},
author = {Eric Amar},
journal = {Annales Polonici Mathematici},
keywords = {Hardy space; Nevanlina class; interpolating sequence; Carleson measure},
language = {eng},
number = {1},
pages = {79-87},
title = {Interpolating sequences, Carleson measures and Wirtinger inequality},
url = {http://eudml.org/doc/280383},
volume = {94},
year = {2008},
}

TY - JOUR
AU - Eric Amar
TI - Interpolating sequences, Carleson measures and Wirtinger inequality
JO - Annales Polonici Mathematici
PY - 2008
VL - 94
IS - 1
SP - 79
EP - 87
AB - 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 $μ_{S}:= ∑_{a∈S} (1-|a|²)ⁿ δ_{a}$ 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 $μ_{S}$ 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 $H^{p}()$, then $μ_{S}$ 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.
LA - eng
KW - Hardy space; Nevanlina class; interpolating sequence; Carleson measure
UR - http://eudml.org/doc/280383
ER -