Cauchy-Poisson transform and polynomial inequalities

Mirosław Baran. "Cauchy-Poisson transform and polynomial inequalities." Annales Polonici Mathematici 95.3 (2009): 199-206. <http://eudml.org/doc/280662>.

@article{MirosławBaran2009,
abstract = {We apply the Cauchy-Poisson transform to prove some multivariate polynomial inequalities. In particular, we show that if the pluricomplex Green function of a fat compact set E in $ℝ^N$ is Hölder continuous then E admits a Szegö type inequality with weight function $dist(x,∂E)^\{-(1-κ)\}$ with a positive κ. This can be viewed as a (nontrivial) generalization of the classical result for the interval E = [-1,1] ⊂ ℝ.},
author = {Mirosław Baran},
journal = {Annales Polonici Mathematici},
keywords = {Cauchy-Poisson transform; polynomal inequality; Bernstein-Szegö type inequality; Zakharyuta-Siciak extremal function; Green function},
language = {eng},
number = {3},
pages = {199-206},
title = {Cauchy-Poisson transform and polynomial inequalities},
url = {http://eudml.org/doc/280662},
volume = {95},
year = {2009},
}

TY - JOUR
AU - Mirosław Baran
TI - Cauchy-Poisson transform and polynomial inequalities
JO - Annales Polonici Mathematici
PY - 2009
VL - 95
IS - 3
SP - 199
EP - 206
AB - We apply the Cauchy-Poisson transform to prove some multivariate polynomial inequalities. In particular, we show that if the pluricomplex Green function of a fat compact set E in $ℝ^N$ is Hölder continuous then E admits a Szegö type inequality with weight function $dist(x,∂E)^{-(1-κ)}$ with a positive κ. This can be viewed as a (nontrivial) generalization of the classical result for the interval E = [-1,1] ⊂ ℝ.
LA - eng
KW - Cauchy-Poisson transform; polynomal inequality; Bernstein-Szegö type inequality; Zakharyuta-Siciak extremal function; Green function
UR - http://eudml.org/doc/280662
ER -