Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

Streszczenie

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 $\Bbb R^N$ is Hölder continuous then $E$ admits a Szegö type inequality with weight function $\text{dist}(x,\partial E)^{-(1-\kappa )}$ with a positive $\kappa$. This can be viewed as a (nontrivial) generalization of the classical result for the interval $E=[-1,1]\subset \Bbb R$.