Cauchy-Poisson transform and polynomial inequalities

• Autorzy: Mirosław Baran
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32U35: Pluricomplex Green functions
• 31C10: Pluriharmonic and plurisubharmonic functions
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2009
• Tom: 95
• Numer: 3
• Strony: 199-206

Daty

wydano

2009

Twórcy

autor

Mirosław Baran

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ap95-3-1