Cauchy-Poisson transform and polynomial inequalities
Mirosław Baran
Annales Polonici Mathematici, Tome 95 (2009), p. 199-206 / Harvested from The Polish Digital Mathematics Library
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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 ℝN 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.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:280662 
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Mirosław Baran. Cauchy-Poisson transform and polynomial inequalities. Annales Polonici Mathematici, Tome 95 (2009) pp. 199-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-1/